Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay
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Marija Milošević [1]
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[1] University of Nis
University of Nis
Serbia
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 248-264
- Idioma: inglés
- DOI: 10.1016/j.cam.2014.12.002
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Resumen
This paper can be regarded as the continuation of the work contained in papers Milošević (2011, 2013). At the same time, it represents the extension of the paper Wu et al. (2010). In this paper, the one-sided Lipschitz condition is employed in the context of the backward Euler method, for a class of neutral stochastic differential equations with constant delay. Sufficient conditions for this method to be well defined are revealed. Under certain nonlinear growth conditions, the convergence in probability is established for the continuous forward–backward Euler method, as well as for the discrete backward Euler method. Additionally, it is proved that the discrete backward Euler equilibrium solution is globally a.s. asymptotically exponentially stable, without requiring for the drift coefficient to satisfy the linear growth condition.
