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Divergence of the backward Euler method for ordinary stochastic differential equations

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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.

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Acknowledgements

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

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  1. Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Marija Milošević

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  1. Marija Milošević
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Correspondence to Marija Milošević.

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The author’s research is supported by Grant No. 174007 of the Ministry of Science, Republic of Serbia.

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Milošević, M. Divergence of the backward Euler method for ordinary stochastic differential equations. Numer Algor 82, 1395–1407 (2019). https://doi.org/10.1007/s11075-019-00661-6

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  • DOI: https://doi.org/10.1007/s11075-019-00661-6

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