ON EXACT CONVERGENCE RATE OF STRONG NUMERICAL SCHEMES FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Title & Authors
ON EXACT CONVERGENCE RATE OF STRONG NUMERICAL SCHEMES FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Nam, Dou-Gu;

Abstract
We propose a simple and intuitive method to derive the exact convergence rate of global $\small{L_{2}-norm}$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $\small{M{\"u}ller-Gronbach\;(2004)}$. 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 $\small{L_{2}-norm}$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.
Keywords
strong approximation of SDE;global $\small{L_2}$-norm error;
Language
English
Cited by
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