DOI QR코드

DOI QR Code

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

  • Nam, Dou-Gu (National Institute for mathematical Sciences)
  • Published : 2007.02.28

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 $M{\"u}ller-Gronbach\;(2004)$. 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 $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

Keywords

strong approximation of SDE;global $L_2$-norm error

References

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