Jump-Diffusions in Hilbert Spaces: Existence, Stability and Numerics - Mathematics > ProbabilityReport as inadecuate




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Abstract: By means of an original approach, called -method of the moving frame-, weestablish existence, uniqueness and stability results for mild and weaksolutions of stochastic partial differential equations SPDEs with pathdependent coefficients driven by an infinite dimensional Wiener process and acompensated Poisson random measure. Our approach is based on a time-dependentcoordinate transform, which reduces a wide class of SPDEs to a class of simplerSDE problems. We try to present the most general results, which we can obtainin our setting, within a self-contained framework to demonstrate our approachin all details. Also several numerical approaches to SPDEs in the spirit ofthis setting are presented.



Author: Damir Filipovic, Stefan Tappe, Josef Teichmann

Source: https://arxiv.org/



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