Weak and strong approximations of reflected diffusions via penalization methods

2012/06/29 by Leszek Slominski, Slominski, Leszek
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1206.7063

arxiv created 2012/06/29 · arxiv updated 2012/07/02

Abstract

We study approximations of reflected Itô diffusions on convex subsets D of \Rd by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly discontinuous) functions. In the case of Lipschitz continuous coefficients we give the rate of L^p approximation for every p≥1. We prove that if D is a convex polyhedron then the rate is O((\fracln nn)^1/2), and in the general case the rate is O((\fracln nn)^1/4).

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