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Axioms 2018, 7(4), 91; https://doi.org/10.3390/axioms7040091

Stability Issues for Selected Stochastic Evolutionary Problems: A Review

1
Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
2
Department of Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy
The authors contributed equally to this work. The authors are members of the INdAM Research group GNCS.
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Author to whom correspondence should be addressed.
Received: 1 May 2018 / Revised: 13 November 2018 / Accepted: 21 November 2018 / Published: 1 December 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Abstract

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 ϑ -methods for Volterra integral equations. View Full-Text
Keywords: stochastic differential equations; stochastic multistep methods; stochastic Volterra integral equations; mean-square stability; asymptotic stability stochastic differential equations; stochastic multistep methods; stochastic Volterra integral equations; mean-square stability; asymptotic stability
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Cardone, A.; Conte, D.; D’Ambrosio, R.; Paternoster, B. Stability Issues for Selected Stochastic Evolutionary Problems: A Review. Axioms 2018, 7, 91.

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