On the Stochastic Magnus Expansion and its Application to SPDEs, 25 February 2020

We derive a stochastic version of the Magnus expansion for the solution of linear systems of Ito stochastic differential equations (SDEs). The goal of this paper is twofold. First, we prove existence and a representation formula for the logarithm associated to the solution of the matrix-valued SDEs. Second,we propose a new method for the numerical solution of stochastic partial differential equations (SPDEs) based on spatial discretization and application of the stochastic Magnus expansion. A notable feature oft he method is that it is fully parallelizable. We also present numerical tests in order to asses the accuracy of the numerical schemes.
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