Mean square convergence of a semidiscrete scheme for SPDEs of Zakai type driven by square integrable martingales

In this short note, a direct proof of L2 convergence of an Euler–Maruyama approximation of a Zakai equation driven by a square integrable martingale is shown. The order of convergence is as known for real-valued stochastic differential equations and for less general driving noises O( √ ∆t) for a time discretization step size ∆t.

• Type: Journal
• Year: 2010
• Where: PROCEDIA
• Authors: Annika Lang
• Keywords: PROCEDIA 2010, Square Integrable Martingale, Stochastic Differential Equations, Zakai Equation