Multiindex Monte Carlo method for semilinear stochastic partial differential equations

Abtract:
In this talk, I will present an exponential-integrator based mulitiindex Monte Carlo method (MIMC) for weak approximations of mild solutions of semilinear stochastic partial differential equations (SPDE). I will present the recent theoretical results on multiindex coupled solutions of the SPDE, namely that such couplings are stable and satisfy multiplicative error estimates, and describe how this theory can be utilized to obtain a tractable MIMC method. Numerical examples show that MIMC outperforms alternative methods, such as multilevel Monte Carlo, in settings with low regularity. I will also briefly discuss another recent work that extends the analysis of the truncated-Milstien scheme with an antithetic estimator to SPDEs.