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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The author is very thankful to the reviewers for their valuable suggestions which improved the paper.
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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
- Ordinary stochastic differential equations
- Backward Euler method
- Strong L p-divergence
- Super-linear growth conditions
- One-sided Lipschitz condition
Mathematics Subject Classification (2010)