Importance sampling techniques for SPDEs: an infinite dimensional approach
Sprache des Vortragstitels:
5th Austrian Stochastics Days
Sprache des Tagungstitel:
In this talk, we consider Monte Carlo-based methods for estimating E[f(X(T))], where X(T) denotes the mild solution of a stochastic partial differential equation (SPDE) at a given time T. It is a well-known result that the resulting Monte Carlo error can be controlled by either enlarging the number of realisations or by applying appropriate variance reduction methods. Obviously, a natural bound on the number of trajectories is imposed by the computational cost of the time integration method, which limits the possibility of increasing the number of numerical
trajectories for high dimensional SODEs - especially for systems arising from semi-discretised SPDEs. For this reason, we present an infinite dimensional approach how importance sampling can be applied to SPDEs in order to reduce the variance of the quantity of interest.