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.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2016, 126 (3), pp.857-882
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Soumis le : lundi 14 novembre 2016 - 16:14:38
Dernière modification le : vendredi 4 janvier 2019 - 17:32:34


  • 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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