An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients

Junxia Duan () and Jun Peng ()
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Junxia Duan: Central South University
Jun Peng: Central South University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 575-602

Abstract: Abstract In this paper, we study a numerical approximation scheme for reflected stochastic differential equations (SDEs) with non-Lipschitzian coefficients in a bounded convex domain. It is shown, under some mild conditions, that the approximation scheme converges in uniform $${{L}}^2 $$ L 2 to the solution of reflected SDEs. Moreover, we move from local to global monotonicity conditions and consider the rate of convergence for our approximation scheme to reflected SDEs with coefficients which have at most polynomial growth.

Keywords: Stochastic differential equations; Reflecting boundary; Non-Lipschitzian coefficients; Penalization Euler scheme; 60H10; 60H30; 65C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01052-7

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