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Weak approximations for martingale representations

Abstract : We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by 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.
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Contributor : Serena Benassù <>
Submitted on : Monday, November 14, 2016 - 4:14:38 PM
Last modification on : Friday, March 27, 2020 - 3:39:21 AM


  • HAL Id : hal-01396590, version 1


Yi Lu, Rama Cont. Weak approximations for martingale representations. Stochastic Processes and their Applications, Elsevier, 2016, 126 (3), pp.857-882. ⟨hal-01396590⟩



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