Almost sure convergence of a semidiscrete Milstein scheme for SPDEs of Zakai type

Journal article, 2010

A semidiscrete Milstein scheme for stochastic partial differential equations of Zakai type on a bounded domain of ℝd is derived. It is shown that the order of convergence of this scheme is 1 for convergence in mean square sense. For almost sure convergence, the order of convergence is proved to be 1 - ε for any ε > 0. © 2010 Taylor & Francis.