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• W1963695507 abstract "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." @default.
• W1963695507 created "2016-06-24" @default.
• W1963695507 creator A5022155844 @default.
• W1963695507 date "2015-05-01" @default.
• W1963695507 modified "2023-09-27" @default.
• W1963695507 title "Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay" @default.
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• W1963695507 doi "https://doi.org/10.1016/j.cam.2014.12.002" @default.
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