کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5776320 1631974 2017 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments
ترجمه فارسی عنوان
همگرایی و پایداری روش تتا تقسیم شده برای معادلات دیفرانسیل تصادفی با استدلال مستقل قطعی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
In this paper, we consider the stochastic differential equations with piecewise continuous arguments (SDEPCAs) in which both the drift and the diffusion coefficients do not satisfy the global Lipschitz and linear growth conditions, especially the diffusion coefficients are highly non-linear growing. It is proved that the split-step theta (SST) method with θ∈[12,1] is strongly convergent to SDEPCAs under the local Lipschitz, monotone and one-sided Lipschitz conditions. It is also obtained that the SST method with θ∈(12,1] preserves the exponential mean square stability of SDEPCAs under the monotone condition and some condition on the step-size. Without any restriction on the step-size, there exists θ∗∈(12,1] such that the SST method with θ∈(θ∗,1] is exponentially stable in mean square. Moreover, for sufficiently small step-size, the rate constant can be reproduced. Some numerical simulations are presented to illustrate the analytical theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 317, June 2017, Pages 55-71
نویسندگان
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