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

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