On the Existence Theory of Hilbert Space valued Diffusion Processes

Günter Hinrichs

Published 2010-08-16Version 1

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.