Weak approximation of martingale representations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Cont, Rama^1,2  Lu, Yi^1,2 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Paris 06, CNRS, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

关键词: Martingale representation;    Semimartingale;    Functional calculus;    Functional Ito calculus;    Clark-Ocone formula;    Malliavin calculus;    Stochastic differential equations;    Euler approximation;   

DOI  :  10.1016/j.spa.2015.10.002

来源: Elsevier

【 摘 要 】

We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by computing a directional derivative of the weak Euler scheme and yield a consistent estimator for the integrand in the martingale representation formula for any square-integrable functional of the solution of an SDE with path-dependent coefficients. Explicit convergence rates are derived for functionals which are Lipschitz-continuous in the supremum norm. Our results require neither the Markov property, nor any differentiability conditions on the functional or the coefficients of the stochastic differential equations involved. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free