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On approximation of solutions of multidimensional SDE's with reflecting boundary conditions

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  • Slominski, Leszek

Abstract

Let D be either a convex domain in d or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman [7] and Saisho [11]. We estimate the rate of Lp convergence for Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary of the form , where W is a d-dimensional Wiener process. As a consequence we give the rate of almost sure convergence for these schemes.

Suggested Citation

  • Slominski, Leszek, 1994. "On approximation of solutions of multidimensional SDE's with reflecting boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 197-219, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:197-219
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    Cited by:

    1. Kanagawa S. & Saisho Y., 2000. "Strong Approximation of Reflecting Brownian Motion Using Penalty Method and its Application to Cumputer Simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 6(2), pages 105-114, December.
    2. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.

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