Pathwise approximation and simulation for the Zakai filtering equation through operator splitting (Q1346980)

Convergence results of operator splitting methods for stochastic partial differential equations are usually stated in terms of \(L^ 2\)- convergence. Here the finite-dimensional Zakai equation is approximated by operator splitting over \(0 \leq \Delta < \cdots < N \Delta = T\). The approximation has the order \(O(\Delta^{1/2 - \varepsilon})\) \((\varepsilon \in ]0, {1 \over 2} \tau])\) with probability 1. Six numerical examples are studied.