On the Existence Theory of Hilbert Space valued Diffusion Processes

Details On the Existence Theory of Hilbert Space valued Diffusion Processes On the Existence Theory of Hilbert Space valued Diffusion Processes

2010-08-16

arxiv.org/abs/1008.2682v1

Mathematics

Probability

43 pages, Diploma thesis

Scientific paper

We prove that the solution of certain linear stochastic differential equations in Hilbert spaces, namely those with bounded operators as well as the conservative stochastic Schr\"odinger equations, can be obtained - along the lines of the Lie-Trotter product formula from semigroup theory - by splitting the equation into a ``deterministic'' and a ``stochastic'' part and alternately applying the corresponding solution flows in an iterative manner to the initial value.

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