کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4627520 | 1631810 | 2014 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay
ترجمه فارسی عنوان
روش عددی مبهم برای معادلات دیفرانسیل خام غیرخطی خنثی با تاخیر وابسته به زمان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
This paper represents the continuation of the analysis from papers MiloÅ¡eviÄ (2011) [10] and MiloÅ¡eviÄ (2013) [11]. The main aim of this paper is to establish certain results for the backward Euler method for a class of neutral stochastic differential equations with time-dependent delay. For that purpose, the split-step backward Euler method, which represents an extension of the backward Euler method, is introduced for this class of equations. Conditions under which the split-step backward Euler method, and thus the backward Euler method, is well defined are revealed. Moreover, the convergence in probability of the backward Euler method is proved under certain nonlinear growth conditions including the one-sided Lipschitz condition. This result is proved using the technique which is based on the application of the continuous-time approximation. For this reason, the discrete forward-backward Euler method is involved since it allows its continuous version to be well defined from the aspect of measurability. The convergence in probability is established for the continuous forward-backward Euler solution, which is essential for proving the same result for both discrete forward-backward and backward Euler methods. Additionally, it is proved that the discrete backward Euler equilibrium solution is globally a.s. asymptotically exponentially stable, without the linear growth condition on the drift coefficient of the equation. As usual, the whole consideration is affected by the presence and properties of the delay function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 244, 1 October 2014, Pages 741-760
Journal: Applied Mathematics and Computation - Volume 244, 1 October 2014, Pages 741-760
نویسندگان
Marija MiloÅ¡eviÄ,