Jump-Diffusions in Hilbert Spaces: Existence, Stability and Numerics

Details Jump-Diffusions in Hilbert Spaces: Existence, Stability and Numerics Jump-Diffusions in Hilbert Spaces: Existence, Stability and Numerics

2008-10-28

arxiv.org/abs/0810.5023v2

Mathematics

Probability

fully revised and extended version

Scientific paper

By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent coefficients driven by an infinite dimensional Wiener process and a compensated Poisson random measure. Our approach is based on a time-dependent coordinate transform, which reduces a wide class of SPDEs to a class of simpler SDE problems. We try to present the most general results, which we can obtain in our setting, within a self-contained framework to demonstrate our approach in all details. Also several numerical approaches to SPDEs in the spirit of this setting are presented.

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