In this talk, we study the numerical approximation of the density of the stochastic heat equation via the accelerated exponential Euler scheme. The existence and smoothness of the density of the numerical solution are proved by means of Malliavin calculus. Based on a priori estimates of the numerical solution, we propose a test function-independent weak convergence analysis, which is crucial to derive the convergence rate of densities. The convergence rate of densities in uniform convergence topology is shown to be exactly 1/2 in nonlinear drift case and nearly 1 in affine drift case.

Chuchu Chen is currently an Associate Professor at Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS). Before joining Chinese Academy of Sciences, she received her PhD degree from AMSS, CAS, and worked as Postdoc at Purdue University and Michigan State University, USA. She is currently engaged in researches on numerical analysis of stochastic partial differential equations, especially on structure-preserving algorithms of stochastic Hamiltonian partial differential equations.