Stochastic evolution equations in weighted L² spaces with jump noise

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Abstract

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.

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