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Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations

Miao Wang, Jiang-lun Wu Orcid Logo

Frontiers of Mathematics in China, Volume: 9, Issue: 3, Pages: 601 - 622

Swansea University Author: Jiang-lun Wu Orcid Logo

DOI (Published version): 10.1007/s11464-014-0364-8

Abstract

Based on a recent result on linking stochastic differential equations on ℝ d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov...

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Published in: Frontiers of Mathematics in China
Published: 2014
Online Access: http://link.springer.com/article/10.1007%2Fs11464-014-0364-8
URI: https://cronfa.swan.ac.uk/Record/cronfa22315
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spelling 2017-02-22T11:20:05.7311553 v2 22315 2015-07-08 Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2015-07-08 SMA Based on a recent result on linking stochastic differential equations on ℝ d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensional stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval. Journal Article Frontiers of Mathematics in China 9 3 601 622 Characterization theorem, Burgers-KPZ type nonlinear equations in infinite dimensions, infinite-dimensional semi-linear stochastic differential equations, Galerkin approximation, path-independence 31 12 2014 2014-12-31 10.1007/s11464-014-0364-8 http://link.springer.com/article/10.1007%2Fs11464-014-0364-8 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2017-02-22T11:20:05.7311553 2015-07-08T09:22:59.4551185 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Miao Wang 1 Jiang-lun Wu 0000-0003-4568-7013 2 0022315-22022017111950.pdf MiaoWangJianglunWu1.pdf 2017-02-22T11:19:50.6770000 Output 238283 application/pdf Accepted Manuscript true 2017-02-22T00:00:00.0000000 false eng
title Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
spellingShingle Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
Jiang-lun Wu
title_short Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
title_full Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
title_fullStr Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
title_full_unstemmed Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
title_sort Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Miao Wang
Jiang-lun Wu
format Journal article
container_title Frontiers of Mathematics in China
container_volume 9
container_issue 3
container_start_page 601
publishDate 2014
institution Swansea University
doi_str_mv 10.1007/s11464-014-0364-8
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://link.springer.com/article/10.1007%2Fs11464-014-0364-8
document_store_str 1
active_str 0
description Based on a recent result on linking stochastic differential equations on ℝ d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensional stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.
published_date 2014-12-31T03:26:33Z
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score 11.013148

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