Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise Coupling

Abstract Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling numerical solutions multilevel hierarchy needed to obtain efficiency gains. In this work, we show indeed also when MLMC stochastic partial differential equations (SPDE) reaction-diffusion type, as can improve rate convergence and thus tractability. method with was developed studied numerically on filtering problems (Chernov Num Math 147:71-125, 2021), prove higher than existing methods. We provide comparisons alternative ideas linear nonlinear SPDE illustrate importance feature.