Support theorems for degenerate stochastic differential equations with jumps and applications

TL;DR

This paper develops support theorems for degenerate stochastic differential equations with jumps and applies these results to characterize path-independence of densities in infinite-dimensional cases.

Contribution

It introduces two new support theorems for degenerate SDEs with jumps and applies one to infinite-dimensional equations for density analysis.

Findings

Established two support theorems under different conditions.

Characterized path-independence of Girsanov densities in infinite-dimensional SDEs.

Abstract

In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions. Secondly, we apply one of our support theorems to a class of degenerate stochastic evolution equations (i.e., infinite-dimensional stochastic differential equations) with jumps to get a characterisation of path-independence for the densities of their Girsanov transformations.