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

Huijie Qiao; Jiang-Lun Wu

doi:10.3934/dcdsb.2018215

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2019, Volume 24, Issue 4: 1449-1467. Doi: 10.3934/dcdsb.2018215

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

Huijie Qiao^1, , and
Jiang-Lun Wu^2,

1.
School of Mathematics, Southeast University, Nanjing, Jiangsu 211189, China
2.
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK

* Corresponding author: Huijie Qiao
* Corresponding author: Huijie Qiao

Received: November 2017

Early access: June 24, 2018

Published online: June 24, 2018

The first author is supported by NSF of China (No. 11001051, 11371352).

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Abstract

Based on a recent result in [13], in this paper, we extend it to stochastic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equations 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.

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Mathematics Subject Classification: Primary: 60H15, 60H30; Secondary: 35R60.

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References

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