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

2017/07/25 by Qiao, Huijie, Wu, Jianglun
#35R60 #60H15 #60H30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1707.07828

Abstract

Based on a recent result on characterising the path-independence of the Girsanov transformation for non-Lipschnitz stochastic differential equations (SDEs) with jumps on R^d, in this paper, we extend our consideration of characterising the path-indpendent property from finite-dimensional SDEs with jumps 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 the 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 partial integro-differential equations.

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