Special Session 109: Stochastic Partial Differential Equations
Contents
Higher order numerical schemes for stochastic differential equations (SODEs) can be derived systematically
using stochastic Taylor expansions based on iterated applications of the It\^o formula. For stochastic partial
differential equations (SPDEs) there is no general It\^o formula that can be used in this way.
Nevertheless higher order temporal expansions for mild solutions of SPDEs are possible using Taylor-like expansions
with an idea that was first used for pathwise random ordinary differential equations (RODEs). This will be
illustrated first for RODEs and then extended to SPDEs. The same relationship between RODEs and SODES as well
as RPDEs and SPDEs will be indicated as well as other issues that arise in their discretization.