Almost sure convergence of a Galerkin approximation for SPDEs of Zakai type driven by square integrable martingales

This work describes a Galerkin type method for stochastic partial differential equations of Zakai type driven by an infinite dimensional càdlàg square integrable martingale. Error estimates in the semidiscrete case, where discretization is only done in space, are derived in LpLp and almost sure senses. Simulations confirm the theoretical results.