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On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces

Huijie Qiao, Jiang-lun Wu Orcid Logo

Discrete & Continuous Dynamical Systems - B, Volume: 24, Issue: 4, Pages: 1449 - 1467

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.3934/dcdsb.2018215

Abstract

Based on a recent result in [14], in this paper, we extend it to stochas- tic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equa- tions with jumps in a manner that one could then lin...

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Published in: Discrete & Continuous Dynamical Systems - B
ISSN: 1553-524X
Published: American Institute of Mathematical Sciences 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa38878
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spelling 2019-01-31T15:04:50.0273337 v2 38878 2018-02-26 On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2018-02-26 SMA Based on a recent result in [14], in this paper, we extend it to stochas- tic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equa- tions with jumps in a manner that one could then link the characterisation of the path- independence for finite-dimensional jump type SDEs to that for the infinite-dimensional settings. Our result provides an intrinsic link of infinite-dimensional stochastic evolution equations with jumps to infinite-dimensional (nonlinear) integro-differential equations. Journal Article Discrete & Continuous Dynamical Systems - B 24 4 1449 1467 American Institute of Mathematical Sciences 1553-524X An Itˆo formula, a Girsanov transformation, path-independence, characterization theorems. 1 4 2019 2019-04-01 10.3934/dcdsb.2018215 http://aimsciences.org/article/doi/10.3934/dcdsb.2018215 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-01-31T15:04:50.0273337 2018-02-26T12:27:31.9512565 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Huijie Qiao 1 Jiang-lun Wu 0000-0003-4568-7013 2 0038878-26022018122830.pdf HuijieQiaoJiang-LunWuPaper2.pdf 2018-02-26T12:28:30.6400000 Output 229077 application/pdf Accepted Manuscript true 2018-02-26T00:00:00.0000000 true eng 0038878-05032018114622.pdf Qiao-Wu.pdf 2018-03-05T11:46:22.3170000 Output 339263 application/pdf Accepted Manuscript true 2019-05-18T00:00:00.0000000 true eng
title On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
spellingShingle On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
Jiang-lun Wu
title_short On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
title_full On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
title_fullStr On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
title_full_unstemmed On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
title_sort On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Huijie Qiao
Jiang-lun Wu
format Journal article
container_title Discrete & Continuous Dynamical Systems - B
container_volume 24
container_issue 4
container_start_page 1449
publishDate 2019
institution Swansea University
issn 1553-524X
doi_str_mv 10.3934/dcdsb.2018215
publisher American Institute of Mathematical Sciences
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://aimsciences.org/article/doi/10.3934/dcdsb.2018215
document_store_str 1
active_str 0
description Based on a recent result in [14], in this paper, we extend it to stochas- tic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equa- tions with jumps in a manner that one could then link the characterisation of the path- independence for finite-dimensional jump type SDEs to that for the infinite-dimensional settings. Our result provides an intrinsic link of infinite-dimensional stochastic evolution equations with jumps to infinite-dimensional (nonlinear) integro-differential equations.
published_date 2019-04-01T03:49:19Z
_version_ 1763752394410164224
score 11.013148

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