Stability Issues for Selected Stochastic Evolutionary Problems: A Review

被引：11
作者：
Cardone, Angelamaria [1 ]
Conte, Dajana [1 ]
D'Ambrosio, Raffaele [2 ]
Paternoster, Beatrice [1 ]
机构：
[1] Univ Salerno, Dept Math, I-84084 Fisciano, Italy
[2] Univ Aquila, Dept Engn & Comp Sci & Math, I-67100 Laquila, Italy
来源：
AXIOMS | 2018年 / 7卷 / 04期
关键词：
stochastic differential equations; stochastic multistep methods; stochastic Volterra integral equations; mean-square stability; asymptotic stability;
D O I：
10.3390/axioms7040091
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We review some recent contributions of the authors regarding the numerical approximation of stochastic problems, mostly based on stochastic differential equations modeling random damped oscillators and stochastic Volterra integral equations. The paper focuses on the analysis of selected stability issues, i.e., the preservation of the long-term character of stochastic oscillators over discretized dynamics and the analysis of mean-square and asymptotic stability properties of theta-methods for Volterra integral equations.
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页数：14
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