Characterizing the path-independence of the Girsanov transformation for non-Lipschitz SDEs with jumps

In the paper, by virtue of the Girsanov transformation, we derive a link of a class of (time-inhomogeneous) non-Lipschitz stochastic differential equations (SDEs) with jumps to a class of semi-linear partial integro-differential equations (PIDEs) of parabolic type, in such a manner that these obtained PIDEs characterize the path-independence property of the density process of Girsanov transformation for the non-Lipschitz SDEs with jumps.