Weak approximation of martingale representations
arXiv:1501.00383 · doi:10.1016/j.spa.2015.10.002
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.
Final version: Sept 2015. Lipschitz assumptions removed, drift coefficient allowed to be non-zero. appears in Stochastic Processes and their Applications, 2015
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