In the paper, we are concerned with degenerate stochastic differential equations with jumps. We first establish two theorems about supports for the solution laws of the degenerate stochastic differential equations, under different (sufficient) conditions. We then apply one of our results to a class of degenerate stochastic evolution equations (that is, stochastic differential equations in infinite dimensions) with jumps to obtain a characterisation of path-independence for the densities of their Girsanov transformations.

中文翻译：

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支持具有跳跃和应用的退化随机微分方程

在本文中，我们关注的是具有跳跃的退化随机微分方程。我们首先建立两个关于在不同（充分）条件下支持退化随机微分方程的解律的定理。然后，我们将我们的一个结果应用于一类具有跳跃的退化随机演化方程（即无限维度的随机微分方程），以获得其 Girsanov 变换密度的路径无关性特征。