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Approximations for stochastic differential equations with reflecting convex boundaries

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  • Pettersson, Roger

Abstract

We consider convergence of a recursive projection scheme for a stochastic differential equation reflecting on the boundary of a convex domain G. If G satisfies Condition (B) in Tanaka (1979), we obtain mean square convergence, pointwise, with the rate O(([delta]log1/[delta])1/2), and if G is a convex polyhedron we obtain mean square convergence, uniformly on compacts, with the rate O([delta]log1/[delta]). An application is given for stochastic differential equations with hysteretic components.

Suggested Citation

  • Pettersson, Roger, 1995. "Approximations for stochastic differential equations with reflecting convex boundaries," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 295-308, October.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:295-308
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    Cited by:

    1. Slominski, Leszek, 2001. "Euler's approximations of solutions of SDEs with reflecting boundary," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 317-337, August.
    2. Pettersson, Roger, 2000. "Projection scheme for stochastic differential equations with convex constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 125-134, July.
    3. 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.
    4. Mei, Hongwei & Yin, George, 2015. "Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3104-3125.
    5. Semrau-Giłka, Alina, 2015. "On approximation of solutions of one-dimensional reflecting SDEs with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 315-321.
    6. 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.
    7. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.

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