Divergence of the backward Euler method for ordinary stochastic differential equations

  • Marija MiloševićEmail author
Original Paper


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.


Ordinary stochastic differential equations Backward Euler method Strong Lp-divergence Super-linear growth conditions One-sided Lipschitz condition 

Mathematics Subject Classification (2010)



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The author is very thankful to the reviewers for their valuable suggestions which improved the paper.


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Authors and Affiliations

  1. 1.Faculty of Science and MathematicsUniversity of NišNišSerbia

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