PUB - Publikationen an der Universität Bielefeld

In this thesis, we study two classes of stochastic differential equations (SDEs in short) with jump noise in weighted L² spaces over $\mathbb{R}^d$. More precisely, the first class of SDEs is a jump-diffusion model in the sense of Merton, i.e. the SDE is driven by a Wiener noise and a Poisson noise. The second class consists of SDE's with Levy noise. We show existence of mild solutions and establish their regularity properties in the case of a drift term consisting of a nonautonomous linear (differential) operator and a non-Lipschitz Nemitskii-type operator.