  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.
