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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

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

Swansea University Author: Jiang-lun Wu

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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
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 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.
Keywords: An Itˆo formula, a Girsanov transformation, path-independence, characterization theorems.
College: Faculty of Science and Engineering
Issue: 4
Start Page: 1449
End Page: 1467

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