Stochastic Equations Driven by Lévy Processes

Abstract

In this thesis we first study a stochastic heat equation driven by Lévy noise and understand the well-posedness of the associated martingale problem. We use the method of duality to establish the same. In the second part of the thesis we explore the method of Algebraic duality and establish weak-uniqueness for a class of infinite dimensional interacting diffusions. We conclude the thesis with some preliminary observations on how to construct path wise stochastic integrals under a Poisson random measure.