Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals

Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals

This paper presents a generalization of the Kunita-Watanabe decomposition of a \(L^2\) space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in \(L^2\). To get the result, a useful relation between the regularity of the martingale family respect...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2019-10
1. Verfasser: Simard, Clarence
Format: Artikel
Sprache:eng
Schlagworte:
Decomposition
Integrals
Martingales
Optimization
Regularity
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Simard, Clarence
description This paper presents a generalization of the Kunita-Watanabe decomposition of a \(L^2\) space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in \(L^2\). To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in \(L^2\). Finally, an example is given where the optimization problem is solved explicitely.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2073917267</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2073917267</sourcerecordid><originalsourceid>FETCH-proquest_journals_20739172673</originalsourceid><addsrcrecordid>eNqNjrEKwjAUAIMgWLT_8MBFh0KaWKuzKA6Ki2OxhJi2KTWv5qX4-3bwA5xuuBtuwiIhZZrsNkLMWEzUcs7FNhdZJiN2uyofrKtVZ-BpNL56JBssOsAKFBSry0MUa6BeaQMfGxpw6DrrjPJAAXWjKFgN1gVTe9XRgk2rESb-cc6Wp-P9cE56j-_BUChbHLwbVSl4LvdpPq7I_6ov-yM-dA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2073917267</pqid></control><display><type>article</type><title>Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals</title><source>Free E- Journals</source><creator>Simard, Clarence</creator><creatorcontrib>Simard, Clarence</creatorcontrib><description>This paper presents a generalization of the Kunita-Watanabe decomposition of a \(L^2\) space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in \(L^2\). To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in \(L^2\). Finally, an example is given where the optimization problem is solved explicitely.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Decomposition ; Integrals ; Martingales ; Optimization ; Regularity</subject><ispartof>arXiv.org, 2019-10</ispartof><rights>2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Simard, Clarence</creatorcontrib><title>Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals</title><title>arXiv.org</title><description>This paper presents a generalization of the Kunita-Watanabe decomposition of a \(L^2\) space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in \(L^2\). To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in \(L^2\). Finally, an example is given where the optimization problem is solved explicitely.</description><subject>Decomposition</subject><subject>Integrals</subject><subject>Martingales</subject><subject>Optimization</subject><subject>Regularity</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjrEKwjAUAIMgWLT_8MBFh0KaWKuzKA6Ki2OxhJi2KTWv5qX4-3bwA5xuuBtuwiIhZZrsNkLMWEzUcs7FNhdZJiN2uyofrKtVZ-BpNL56JBssOsAKFBSry0MUa6BeaQMfGxpw6DrrjPJAAXWjKFgN1gVTe9XRgk2rESb-cc6Wp-P9cE56j-_BUChbHLwbVSl4LvdpPq7I_6ov-yM-dA</recordid><startdate>20191001</startdate><enddate>20191001</enddate><creator>Simard, Clarence</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20191001</creationdate><title>Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals</title><author>Simard, Clarence</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20739172673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Decomposition</topic><topic>Integrals</topic><topic>Martingales</topic><topic>Optimization</topic><topic>Regularity</topic><toplevel>online_resources</toplevel><creatorcontrib>Simard, Clarence</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Simard, Clarence</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals</atitle><jtitle>arXiv.org</jtitle><date>2019-10-01</date><risdate>2019</risdate><eissn>2331-8422</eissn><abstract>This paper presents a generalization of the Kunita-Watanabe decomposition of a \(L^2\) space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in \(L^2\). To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in \(L^2\). Finally, an example is given where the optimization problem is solved explicitely.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2019-10
issn 2331-8422
language eng
recordid cdi_proquest_journals_2073917267
source Free E- Journals
subjects Decomposition
Integrals
Martingales
Optimization
Regularity
title Martingale decomposition of a \(L^2\) space with nonlinear stochastic integrals
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T23%3A15%3A41IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Martingale%20decomposition%20of%20a%20%5C(L%5E2%5C)%20space%20with%20nonlinear%20stochastic%20integrals&rft.jtitle=arXiv.org&rft.au=Simard,%20Clarence&rft.date=2019-10-01&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2073917267%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2073917267&rft_id=info:pmid/&rfr_iscdi=true