Variance reduction techniques for the numerical simulation of the stochastic heat equation
Sprache des Vortragstitels:
We consider a finite dimensional version of the stochastic heat equation (obtained by spatial discretisation) which is subject to multiplicative Q-Wiener noise. For growing diffusion parameter the equilibrium solution of the system eventually gets mean-square unstable, however it takes an unreasonably large number of numerical trajectories to see this instability in Monte-Carlo simulation. We will discuss the practicability and the influence of variance reduction techniques, namely importance sampling via Girsanov's theorem and control variates, on the Monte-Carlo estimation. This talk is based on joint work with E. Buckwar and A. Thalhammer and connected with the talk "Computational mean-square stability analysis for linear systems of SODEs" by A. Thalhammer, which treats the interplay of different stability concepts in numerical simulation.