On exact convergence rate of strong numerical schemes for stochastic differential equations
Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 125-130 Printed March 1, 2007
Dougu Nam National Institute for Mathematical Sciences
Abstract : We propose a simple and intuitive method to derive the exact convergence rate of global $L_2$-norm error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and M\"uller-Gronbach (2004). We conclude that any strong numerical scheme of order $\gamma>1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_2$-norm error and is similarly applicable for evaluating the convergence rate of global uniform approximations.
Keywords : strong approximation of SDE, global $L_2$-norm error