Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift |
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Authors: | Ali Foroush Bastani Mahdieh Tahmasebi |
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Institution: | a Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iranb Department of Mathematics, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran |
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Abstract: | In this paper, we are concerned with the numerical approximation of stochastic differential equations with discontinuous/nondifferentiable drifts. We show that under one-sided Lipschitz and general growth conditions on the drift and global Lipschitz condition on the diffusion, a variant of the implicit Euler method known as the split-step backward Euler (SSBE) method converges with strong order of one half to the true solution. Our analysis relies on the framework developed in D. J. Higham, X. Mao and A. M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM Journal on Numerical Analysis, 40 (2002) 1041-1063] and exploits the relationship which exists between explicit and implicit Euler methods to establish the convergence rate results. |
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Keywords: | primary 60H10 secondary 60H35 |
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