Parametric family of SDEs driven by L\'evy noise

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 ${\mathcal{S}}^{\mathrm{\prime }}$. 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].