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Weak and strong approximations of reflected diffusions via penalization methods

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  • Słomiński, Leszek

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 functions. In the case of Lipschitz continuous coefficients we give the rate of Lp approximation for every p≥1. We prove that if D is a convex polyhedron then the rate is O((lnnn)1/2), and in the general case the rate is O((lnnn)1/4).

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  • Słomiński, Leszek, 2013. "Weak and strong approximations of reflected diffusions via penalization methods," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 752-763.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:752-763
    DOI: 10.1016/j.spa.2012.10.006
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    Keywords

    Reflected diffusions; Penalization methods;

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