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

摘要

Based on a recent result on characterising the path-independence of theGirsanov transformation for non-Lipschnitz stochastic differential equations(SDEs) with jumps on $R^d$, in this paper, we extend our consideration ofcharacterising the path-indpendent property from finite-dimensional SDEs withjumps to stochastic evolution equations with jumps in Hilbert spaces. This isdone via Galerkin type finite-dimensional approximations of theinfinite-dimensional stochastic evolution equations with jumps in the mannerthat one could then link the characterisation of the path-independence forfinite-dimensional jump type SDEs to that for the infinite-dimensionalsettings. Our result provides an intrinsic link of infinite-dimensionalstochastic evolution equations with jumps to infinite-dimensional partialintegro-differential equations.