Divergence of the backward Euler method for ordinary stochastic differential equations
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This paper is based on the analysis of the backward Euler method for stochastic differential equations. It is motivated by the paper (Hutzenthaler et al. Proc. R. Soc. A 467, 1563–1576, 2011), where authors studied the equations with superlinearly growing coefficients. The main goal of this paper is to reveal sufficient conditions of the strong and weak Lp-divergence of the backward Euler method at finite time, for all \(p\in (0,\infty )\). Theoretical results are supported by examples.
KeywordsOrdinary stochastic differential equations Backward Euler method Strong Lp-divergence Super-linear growth conditions One-sided Lipschitz condition
Mathematics Subject Classification (2010)60H10
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The author is very thankful to the reviewers for their valuable suggestions which improved the paper.
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