Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:282

Article

Przybylowicz, Pawel

关键词: Non-standard assumptions;    One-point approximation;    Lower bounds;    Asymptotic error;    Optimal algorithm;    Monte Carlo methods;   

DOI  :  10.1016/j.cam.2015.01.003

来源: Elsevier

【 摘 要 】

We consider strong one-point approximation of solutions of scalar stochastic differential equations (SDEs) with irregular coefficients. The drift coefficient a : [0, T] x R -> R is assumed to be Lipschitz continuous with respect to the space variable but only measurable with respect to the time variable. For the diffusion coefficient b : [0, T] -> R we assume that it is only piecewise Holder continuous with Holder exponent Q is an element of (0,1]. We show that, roughly speaking, the error of any algorithm, which uses n values of the diffusion coefficient, cannot converge to zero faster than n(-min)[Q, 1/2] as n -> +infinity. This best speed of convergence is achieved by the randomized Euler scheme. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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