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Divergence of the backward Euler method for ordinary stochastic differential equations

  • Marija MiloševićEmail author
Original Paper
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Abstract

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.

Keywords

Ordinary 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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Notes

Acknowledgements

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

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Science and MathematicsUniversity of NišNišSerbia

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