Computational and Applied Mathematics seminar

Abstract: We present an exponential-integrator based multi-index Monte Carlo method (MIMC) for weak approximations of semilinear stochastic partial differential equations (SPDE). We explore recent theoretical results on multi-index-coupled solutions of SPDEs, showing that such couplings are stable and satisfy multiplicative error estimates, and describe how this theory can be utilized to produce a tractable Monte Carlo method for weak approximations. Numerical examples illustrating the performance of MIMC will also be included.