Mathematics Seminar 09/14/23

Abstract:  Stochastic partial differential equations (SPDEs) are generalized from PDEs by random force terms and coefficients. SPDEs have been a subject of interest in recent years for their widespread application in quantum field theory, statistical mechanics, and spatial modeling. In this talk, stochastic Allen-Cahn-type equation (a 1+1-dimensional space-time PDEs driven by space-time white noise) and its approximation by a fully discrete space-time explicit finite difference scheme are studied. Many previous results have indicated that a strong convergence rate of 1/2 with respect to the parabolic grid is predicted to be ideal. However, one can reach almost sure convergence of rate 1 (and no better) when measuring the error in appropriate distributional norm.