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Calculated Shard: 158 (from laksa107)

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curl -X POST \
  'http://laksa158.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://eudml.org/doc/40503\')), getAhrefsUnparsedNoserviceFromURL(\'https://eudml.org/doc/40503\'))) FORMAT JSONEachRow'

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{"found_url":"https:\/\/eudml.org\/doc\/40503","crawl_time":1773246008,"first_indexed_time":1437273248,"http_code":200,"src_unparsed":"org,eudml!\/doc\/40503 s443","src_root_hash":"127728573952213358","history_drop_reason":null,"meta_title":"EUDML | On the Karhunen-Loeve expansion for transformed processes.","meta_descriptions":[],"attrs_boilerpipe_text":"Ramón Gutiérrez Jáimez\n;\nMariano J. Valderrama Bonnet\nTrabajos de Estadística\n(1987)\nVolume: 2, Issue: 2, page 81-90\nISSN: 0213-8190\nAccess Full Article\ntop\n \nAccess to full text\nAbstract\ntop\nWe discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.\nHow to cite\ntop\nGutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. \"On the Karhunen-Loeve expansion for transformed processes..\"\nTrabajos de Estadística\n2.2 (1987): 81-90. <http:\/\/eudml.org\/doc\/40503>.\n@article{GutiérrezJáimez1987,\nabstract = {We discuss the influence of the transformation \\{X(t)\\} → \\{f(t) X(τ(t))\\} on the Karhunen-Loève expansion of \\{X(t)\\}. Our main result is that, in general, the Karhunen-Loève expansion of \\{X(t)\\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \\{f(t) X(τ(t))\\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.},\nauthor = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.},\njournal = {Trabajos de Estadística},\nkeywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process},\nlanguage = {eng},\nnumber = {2},\npages = {81-90},\ntitle = {On the Karhunen-Loeve expansion for transformed processes.},\nurl = {http:\/\/eudml.org\/doc\/40503},\nvolume = {2},\nyear = {1987},\n}\nTY  - JOUR\nAU  - Gutiérrez Jáimez, Ramón\nAU  - Valderrama Bonnet, Mariano J.\nTI  - On the Karhunen-Loeve expansion for transformed processes.\nJO  - Trabajos de Estadística\nPY  - 1987\nVL  - 2\nIS  - 2\nSP  - 81\nEP  - 90\nAB  - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.\nLA  - eng\nKW  - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process\nUR  - http:\/\/eudml.org\/doc\/40503\nER  -\nCitations in EuDML Documents\ntop\nMátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges\nNotes\nEmbed\n?\ntop\nYou must be logged in to post comments.","attrs_markdown":"![](http:\/\/eudml.org\/piwik\/piwik.php?idsite=4)\n\n[Skip to main content (access key 's')](https:\/\/eudml.org\/doc\/40503#content), [Skip to navigation (access key 'n')](https:\/\/eudml.org\/doc\/40503#unit-primary-navigation), [Accessibility information (access key '0')](https:\/\/eudml.org\/about\/accessibility\/)\n\n[EuDML - The European Digital Mathematics Library](https:\/\/eudml.org\/)\n\n[Login](https:\/\/eudml.org\/loginForm)  \\|  [Register](https:\/\/eudml.org\/register)  \\|  [(Why Register?)](https:\/\/eudml.org\/whyRegister)\n\n- [Home](https:\/\/eudml.org\/ \"Home\")\n- [Advanced Search](https:\/\/eudml.org\/search \"Advanced Search\")\n- [Browse by Subject](https:\/\/eudml.org\/subjects\/MSC \"Browse by Subject\")\n- [Browse by Journals](https:\/\/eudml.org\/journals \"Browse by Journals\")\n- [Refs Lookup](https:\/\/eudml.org\/refsLookup \"Refs Lookup\")\n\n# On the Karhunen-Loeve expansion for transformed processes.\n[Ramón Gutiérrez Jáimez](https:\/\/eudml.org\/search\/page?q=sc.general*op.AND*l_0*c_0author_0eq%253A1.Ram%25C3%25B3n+Guti%25C3%25A9rrez+J%25C3%25A1imez&qt=SEARCH); [Mariano J. Valderrama Bonnet](https:\/\/eudml.org\/search\/page?q=sc.general*op.AND*l_0*c_0author_0eq%253A1.Mariano+J.+Valderrama+Bonnet&qt=SEARCH)\n\n[Trabajos de Estadística](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A\/journal\/10033) (1987)\n\n- Volume: 2, Issue: 2, page 81-90\n- ISSN: 0213-8190\n\n## Access Full Article\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\n![icon representing file type: icon-html.png](https:\/\/eudml.org\/assets\/images\/icon-html.png) [Access to full text](http:\/\/dmle.icmat.es\/revistas\/detalle.php?numero=3116)\n\n## Abstract\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\nWe discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.\n\n## How to cite\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\n- [MLA](https:\/\/eudml.org\/doc\/40503#tab-1)\n- [BibTeX](https:\/\/eudml.org\/doc\/40503#tab-2)\n- [RIS](https:\/\/eudml.org\/doc\/40503#tab-3)\n\nGutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. \"On the Karhunen-Loeve expansion for transformed processes..\" Trabajos de Estadística 2.2 (1987): 81-90. \\<http:\/\/eudml.org\/doc\/40503\\>.\n\n@article{GutiérrezJáimez1987,  \n abstract = {We discuss the influence of the transformation \\\\{X(t)\\\\} → \\\\{f(t) X(τ(t))\\\\} on the Karhunen-Loève expansion of \\\\{X(t)\\\\}. Our main result is that, in general, the Karhunen-Loève expansion of \\\\{X(t)\\\\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \\\\{f(t) X(τ(t))\\\\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.},  \n author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.},  \n journal = {Trabajos de Estadística},  \n keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process},  \n language = {eng},  \n number = {2},  \n pages = {81-90},  \n title = {On the Karhunen-Loeve expansion for transformed processes.},  \n url = {http:\/\/eudml.org\/doc\/40503},  \n volume = {2},  \n year = {1987},  \n}\n\nTY - JOUR  \nAU - Gutiérrez Jáimez, Ramón  \nAU - Valderrama Bonnet, Mariano J.  \nTI - On the Karhunen-Loeve expansion for transformed processes.  \nJO - Trabajos de Estadística  \nPY - 1987  \nVL - 2  \nIS - 2  \nSP - 81  \nEP - 90  \nAB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.  \nLA - eng  \nKW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process  \nUR - http:\/\/eudml.org\/doc\/40503  \nER -\n\n## Citations in EuDML Documents\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\n1. [Mátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A\/doc\/269585)\n\n## Notes[Embed](https:\/\/eudml.org\/doc\/40503) [?](https:\/\/eudml.org\/doc\/40503)\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\nYou must be logged in to post comments.\n\n- [Access Full Article](https:\/\/eudml.org\/doc\/40503#content)\n- [Abstract](https:\/\/eudml.org\/doc\/40503#abstract)\n- [How to cite](https:\/\/eudml.org\/doc\/40503#citations)\n- [Citations in EuDML Documents](https:\/\/eudml.org\/doc\/40503#reverseReferences)\n- [Notes](https:\/\/eudml.org\/doc\/40503#notes)\n\n### Article Keywords\nDesarrollo en serie de funciones, Aplicaciones, Procesos de Wiener, Movimiento browniano, Gaussian process, Karhunen-Loève expansion, Wiener process, Brownian bridge, Ornstein-Uhlenbeck process\n\n[Suggest a Subject](https:\/\/eudml.org\/doc\/40503 \"Suggest a Subject\")\n\n### Subjects\nYou must be logged in to add subjects.\n\n#### Stochastic processes\n60G12\n\n[General second-order processes](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20\/subject\/MSC\/60G12)\n\n60G15\n\n[Gaussian processes](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20\/subject\/MSC\/60G15)\n#### Fredholm integral equations\n45B05\n\n[Fredholm integral equations](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20\/subject\/MSC\/45B05)\n\n[Find Similar Documents](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A\/similar\/doc\/40503 \"Find similar documents\")\n\n### From the Journal\n[Trabajos de Estadística](https:\/\/eudml.org\/doc\/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A\/journal\/10033) (1987)\n\n### In Other Databases\n[DML-E](http:\/\/dmle.icmat.es\/revistas\/detalle.php?numero=3116)\n\n[ZBMath](http:\/\/www.zentralblatt-math.org\/zmath\/en\/search\/?q=an:0734.60042)\n\n### On Google Scholar\n- [Articles by Ramón Gutiérrez Jáimez](http:\/\/scholar.google.pl\/scholar?q=author%3A\"Ram%C3%B3n+Guti%C3%A9rrez+J%C3%A1imez\" \"googleScholar.articlesBy\")\n- [Articles by Mariano J. Valderrama Bonnet](http:\/\/scholar.google.pl\/scholar?q=author%3A\"Mariano+J.+Valderrama+Bonnet\" \"googleScholar.articlesBy\")\n\n- [Search for Related Content](http:\/\/scholar.google.pl\/scholar?q=related:https:\/\/eudml.org\/doc\/40503 \"article.details.scholar.button\")\n\n[Add to Personal Lists](https:\/\/eudml.org\/doc\/40503 \"Add to My Lists\")\n\nYou must be logged in to use personal lists.\n\n## Infobox\nTo add items to a personal list choose the desired list from the selection box or create a new list.\n\nTo close, click the Close button or press the ESC key.\n\nClose\n\n## Infobox\nThis article was successfully added to the collection.\n\nTo close, click the Close button or press the ESC key.\n\nClose\n\n### Share this Article\n- [Email to a Colleague](\"Email to a Colleague\")\n- [Mendeley](\"Mendeley\")\n- [CiteULike](\"CiteULike\")\n- [BibSonomy](http:\/\/www.bibsonomy.org\/ShowBookmarkEntry?c=b&jump=yes&url=https%3A%2F%2Feudml.org%2Fdoc%2F40503&description=EUDML%20%C2%A0%7C%C2%A0%20On%20the%20Karhunen-Loeve%20expansion%20for%20transformed%20processes. \"BibSonomy\")\n\n[Tweet](https:\/\/twitter.com\/share)\n\n[EuDML](http:\/\/initiative.eudml.org\/)\n\n- [About EuDML initiative](http:\/\/initiative.eudml.org\/)\n- [Feedback](mailto:helpdesk@eudml.org)\n- version 2.1.7\n\nYour EuDML widget code:[close](https:\/\/eudml.org\/doc\/40503)\n\nTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.","attrs_readable_markdown":"[Ramón Gutiérrez Jáimez](https:\/\/eudml.org\/search\/page?q=sc.general*op.AND*l_0*c_0author_0eq%253A1.Ram%25C3%25B3n+Guti%25C3%25A9rrez+J%25C3%25A1imez&qt=SEARCH); [Mariano J. Valderrama Bonnet](https:\/\/eudml.org\/search\/page?q=sc.general*op.AND*l_0*c_0author_0eq%253A1.Mariano+J.+Valderrama+Bonnet&qt=SEARCH)\n\n[Trabajos de Estadística](https:\/\/eudml.org\/journal\/10033) (1987)\n\n- Volume: 2, Issue: 2, page 81-90\n- ISSN: 0213-8190\n\n## Access Full Article\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\n![icon representing file type: icon-html.png](https:\/\/eudml.org\/assets\/images\/icon-html.png) [Access to full text](http:\/\/dmle.icmat.es\/revistas\/detalle.php?numero=3116)\n\n## Abstract\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\nWe discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.\n\n## How to cite\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\nGutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. \"On the Karhunen-Loeve expansion for transformed processes..\" Trabajos de Estadística 2.2 (1987): 81-90. \\<http:\/\/eudml.org\/doc\/40503\\>.\n\n@article{GutiérrezJáimez1987,  \n abstract = {We discuss the influence of the transformation \\\\{X(t)\\\\} → \\\\{f(t) X(τ(t))\\\\} on the Karhunen-Loève expansion of \\\\{X(t)\\\\}. Our main result is that, in general, the Karhunen-Loève expansion of \\\\{X(t)\\\\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \\\\{f(t) X(τ(t))\\\\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.},  \n author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.},  \n journal = {Trabajos de Estadística},  \n keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process},  \n language = {eng},  \n number = {2},  \n pages = {81-90},  \n title = {On the Karhunen-Loeve expansion for transformed processes.},  \n url = {http:\/\/eudml.org\/doc\/40503},  \n volume = {2},  \n year = {1987},  \n}\n\nTY - JOUR  \nAU - Gutiérrez Jáimez, Ramón  \nAU - Valderrama Bonnet, Mariano J.  \nTI - On the Karhunen-Loeve expansion for transformed processes.  \nJO - Trabajos de Estadística  \nPY - 1987  \nVL - 2  \nIS - 2  \nSP - 81  \nEP - 90  \nAB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.  \nLA - eng  \nKW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process  \nUR - http:\/\/eudml.org\/doc\/40503  \nER -\n\n## Citations in EuDML Documents\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\n1. [Mátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges](https:\/\/eudml.org\/doc\/269585)\n\n## Notes[Embed](https:\/\/eudml.org\/doc\/40503) [?](https:\/\/eudml.org\/doc\/40503)\n[top](https:\/\/eudml.org\/doc\/40503 \"top\")\n\nYou must be logged in to post comments.","meta_canonical":null}

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Boilerpipe Text	Ramón Gutiérrez Jáimez ; Mariano J. Valderrama Bonnet Trabajos de Estadística (1987) Volume: 2, Issue: 2, page 81-90 ISSN: 0213-8190 Access Full Article top Access to full text Abstract top We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. How to cite top Gutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. "On the Karhunen-Loeve expansion for transformed processes.." Trabajos de Estadística 2.2 (1987): 81-90. <http://eudml.org/doc/40503>. @article{GutiérrezJáimez1987, abstract = {We discuss the influence of the transformation \{X(t)\} → \{f(t) X(τ(t))\} on the Karhunen-Loève expansion of \{X(t)\}. Our main result is that, in general, the Karhunen-Loève expansion of \{X(t)\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \{f(t) X(τ(t))\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.}, author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.}, journal = {Trabajos de Estadística}, keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process}, language = {eng}, number = {2}, pages = {81-90}, title = {On the Karhunen-Loeve expansion for transformed processes.}, url = {http://eudml.org/doc/40503}, volume = {2}, year = {1987}, } TY - JOUR AU - Gutiérrez Jáimez, Ramón AU - Valderrama Bonnet, Mariano J. TI - On the Karhunen-Loeve expansion for transformed processes. JO - Trabajos de Estadística PY - 1987 VL - 2 IS - 2 SP - 81 EP - 90 AB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. LA - eng KW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process UR - http://eudml.org/doc/40503 ER - Citations in EuDML Documents top Mátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges Notes Embed ? top You must be logged in to post comments.
Markdown	![](http://eudml.org/piwik/piwik.php?idsite=4) [Skip to main content (access key 's')](https://eudml.org/doc/40503#content), [Skip to navigation (access key 'n')](https://eudml.org/doc/40503#unit-primary-navigation), [Accessibility information (access key '0')](https://eudml.org/about/accessibility/) [EuDML - The European Digital Mathematics Library](https://eudml.org/) [Login](https://eudml.org/loginForm) \\| [Register](https://eudml.org/register) \\| [(Why Register?)](https://eudml.org/whyRegister) - [Home](https://eudml.org/ "Home") - [Advanced Search](https://eudml.org/search "Advanced Search") - [Browse by Subject](https://eudml.org/subjects/MSC "Browse by Subject") - [Browse by Journals](https://eudml.org/journals "Browse by Journals") - [Refs Lookup](https://eudml.org/refsLookup "Refs Lookup") # On the Karhunen-Loeve expansion for transformed processes. [Ramón Gutiérrez Jáimez](https://eudml.org/search/page?q=sc.generalop.ANDl_0c_0author_0eq%253A1.Ram%25C3%25B3n+Guti%25C3%25A9rrez+J%25C3%25A1imez&qt=SEARCH); [Mariano J. Valderrama Bonnet](https://eudml.org/search/page?q=sc.generalop.ANDl_0c_0author_0eq%253A1.Mariano+J.+Valderrama+Bonnet&qt=SEARCH) [Trabajos de Estadística](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A/journal/10033) (1987) - Volume: 2, Issue: 2, page 81-90 - ISSN: 0213-8190 ## Access Full Article [top](https://eudml.org/doc/40503 "top") ![icon representing file type: icon-html.png](https://eudml.org/assets/images/icon-html.png) [Access to full text](http://dmle.icmat.es/revistas/detalle.php?numero=3116) ## Abstract [top](https://eudml.org/doc/40503 "top") We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. ## How to cite [top](https://eudml.org/doc/40503 "top") - [MLA](https://eudml.org/doc/40503#tab-1) - [BibTeX](https://eudml.org/doc/40503#tab-2) - [RIS](https://eudml.org/doc/40503#tab-3) Gutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. "On the Karhunen-Loeve expansion for transformed processes.." Trabajos de Estadística 2.2 (1987): 81-90. \<http://eudml.org/doc/40503\>. @article{GutiérrezJáimez1987, abstract = {We discuss the influence of the transformation \\{X(t)\\} → \\{f(t) X(τ(t))\\} on the Karhunen-Loève expansion of \\{X(t)\\}. Our main result is that, in general, the Karhunen-Loève expansion of \\{X(t)\\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \\{f(t) X(τ(t))\\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.}, author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.}, journal = {Trabajos de Estadística}, keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process}, language = {eng}, number = {2}, pages = {81-90}, title = {On the Karhunen-Loeve expansion for transformed processes.}, url = {http://eudml.org/doc/40503}, volume = {2}, year = {1987}, } TY - JOUR AU - Gutiérrez Jáimez, Ramón AU - Valderrama Bonnet, Mariano J. TI - On the Karhunen-Loeve expansion for transformed processes. JO - Trabajos de Estadística PY - 1987 VL - 2 IS - 2 SP - 81 EP - 90 AB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. LA - eng KW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process UR - http://eudml.org/doc/40503 ER - ## Citations in EuDML Documents [top](https://eudml.org/doc/40503 "top") 1. [Mátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A/doc/269585) ## Notes[Embed](https://eudml.org/doc/40503) [?](https://eudml.org/doc/40503) [top](https://eudml.org/doc/40503 "top") You must be logged in to post comments. - [Access Full Article](https://eudml.org/doc/40503#content) - [Abstract](https://eudml.org/doc/40503#abstract) - [How to cite](https://eudml.org/doc/40503#citations) - [Citations in EuDML Documents](https://eudml.org/doc/40503#reverseReferences) - [Notes](https://eudml.org/doc/40503#notes) ### Article Keywords Desarrollo en serie de funciones, Aplicaciones, Procesos de Wiener, Movimiento browniano, Gaussian process, Karhunen-Loève expansion, Wiener process, Brownian bridge, Ornstein-Uhlenbeck process [Suggest a Subject](https://eudml.org/doc/40503 "Suggest a Subject") ### Subjects You must be logged in to add subjects. #### Stochastic processes 60G12 [General second-order processes](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20/subject/MSC/60G12) 60G15 [Gaussian processes](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20/subject/MSC/60G15) #### Fredholm integral equations 45B05 [Fredholm integral equations](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%09%09%09%20%20%20%20%20%20%20%20%20%20%20%20%0A%09%09%09%20%20%20%20%20%20%20%20/subject/MSC/45B05) [Find Similar Documents](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A/similar/doc/40503 "Find similar documents") ### From the Journal [Trabajos de Estadística](https://eudml.org/doc/%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A%0A/journal/10033) (1987) ### In Other Databases [DML-E](http://dmle.icmat.es/revistas/detalle.php?numero=3116) [ZBMath](http://www.zentralblatt-math.org/zmath/en/search/?q=an:0734.60042) ### On Google Scholar - [Articles by Ramón Gutiérrez Jáimez](http://scholar.google.pl/scholar?q=author%3A"Ram%C3%B3n+Guti%C3%A9rrez+J%C3%A1imez" "googleScholar.articlesBy") - [Articles by Mariano J. 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Readable Markdown	[Ramón Gutiérrez Jáimez](https://eudml.org/search/page?q=sc.generalop.ANDl_0c_0author_0eq%253A1.Ram%25C3%25B3n+Guti%25C3%25A9rrez+J%25C3%25A1imez&qt=SEARCH); [Mariano J. Valderrama Bonnet](https://eudml.org/search/page?q=sc.generalop.ANDl_0c_0author_0eq%253A1.Mariano+J.+Valderrama+Bonnet&qt=SEARCH) [Trabajos de Estadística](https://eudml.org/journal/10033) (1987) - Volume: 2, Issue: 2, page 81-90 - ISSN: 0213-8190 ## Access Full Article [top](https://eudml.org/doc/40503 "top") ![icon representing file type: icon-html.png](https://eudml.org/assets/images/icon-html.png) [Access to full text](http://dmle.icmat.es/revistas/detalle.php?numero=3116) ## Abstract [top](https://eudml.org/doc/40503 "top") We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. ## How to cite [top](https://eudml.org/doc/40503 "top") Gutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. "On the Karhunen-Loeve expansion for transformed processes.." Trabajos de Estadística 2.2 (1987): 81-90. \<http://eudml.org/doc/40503\>. @article{GutiérrezJáimez1987, abstract = {We discuss the influence of the transformation \\{X(t)\\} → \\{f(t) X(τ(t))\\} on the Karhunen-Loève expansion of \\{X(t)\\}. Our main result is that, in general, the Karhunen-Loève expansion of \\{X(t)\\} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of \\{f(t) X(τ(t))\\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.}, author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.}, journal = {Trabajos de Estadística}, keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process}, language = {eng}, number = {2}, pages = {81-90}, title = {On the Karhunen-Loeve expansion for transformed processes.}, url = {http://eudml.org/doc/40503}, volume = {2}, year = {1987}, } TY - JOUR AU - Gutiérrez Jáimez, Ramón AU - Valderrama Bonnet, Mariano J. TI - On the Karhunen-Loeve expansion for transformed processes. JO - Trabajos de Estadística PY - 1987 VL - 2 IS - 2 SP - 81 EP - 90 AB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process. LA - eng KW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process UR - http://eudml.org/doc/40503 ER - ## Citations in EuDML Documents [top](https://eudml.org/doc/40503 "top") 1. [Mátyás Barczy, Endre Iglói, Karhunen-Loève expansions of α-Wiener bridges](https://eudml.org/doc/269585) ## Notes[Embed](https://eudml.org/doc/40503) [?](https://eudml.org/doc/40503) [top](https://eudml.org/doc/40503 "top") You must be logged in to post comments.
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