  In this article we study the existence and uniqueness of strong solutions of
a class of parameterized family of SDEs driven by L\'evy noise. These SDEs
occurs in connection with a class of stochastic PDEs, which take values in the
space of tempered distributions $\mathcal{S}^\prime$. 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].
