  In this article we show that a finite dimensional stochastic differential
equation driven by a L\'evy process can be formulated as a stochastic partial
differential equation. We prove the existence and uniqueness of strong
solutions of such stochastic PDEs. The solutions that we construct have the
`translation invariance' property. The special case of this correspondence for
diffusion processes was proved in [Rajeev, Translation invariant diffusion in
the space of tempered distributions, Indian J. Pure Appl. Math. 44 (2013),
no.~2, 231--258].
