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On approximation of solutions of one-dimensional reflecting SDEs with discontinuous coefficients

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  • Semrau-Giłka, Alina

Abstract

For stochastic differential equations reflecting on the boundary of a connected interval in R we discuss the problem of approximation for solutions. The main results are convergence in law as well as in Lp of discrete schemes that fundamentally generalize the classical Euler and Euler–Peano schemes considered in Semrau-Giłka (2013). The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure and the diffusion coefficient may degenerate on some subsets of the domain. New generalized inequalities of Krylov’s type for stochastic integrals are crucial tools used in the proofs.

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  • 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.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:315-321
    DOI: 10.1016/j.spl.2014.10.011
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    References listed on IDEAS

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    1. Zhang, Tu-Sheng, 1994. "On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 135-147, March.
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    5. Krylov, N. V. & Liptser, R., 2002. "On diffusion approximation with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 235-264, December.
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