Parametric family of SDEs driven by Lévy noise

Abstract

In this article we study the existence and uniqueness of strong solutions of a class of parameterized family of SDEs driven by Lévy 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].