Stability Issues for Selected Stochastic Evolutionary Problems: A Review

Stability Issues for Selected Stochastic Evolutionary Problems: A Review

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 is...

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Main Authors: Angelamaria Cardone, Dajana Conte, Raffaele D’Ambrosio, Beatrice Paternoster
Format: Article
Language:English
Published: MDPI AG 2018-12-01
Series:Axioms
Subjects:
stochastic differential equations
stochastic multistep methods
stochastic Volterra integral equations
mean-square stability
asymptotic stability
Online Access:https://www.mdpi.com/2075-1680/7/4/91
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spelling doaj-bf342374ce1b41e5baecc6a69c2d9d772020-11-25T00:45:51ZengMDPI AGAxioms2075-16802018-12-01749110.3390/axioms7040091axioms7040091Stability Issues for Selected Stochastic Evolutionary Problems: A ReviewAngelamaria Cardone0Dajana Conte1Raffaele D’Ambrosio2Beatrice Paternoster3Department of Mathematics, University of Salerno, 84084 Fisciano, ItalyDepartment of Mathematics, University of Salerno, 84084 Fisciano, ItalyDepartment of Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, ItalyDepartment of Mathematics, University of Salerno, 84084 Fisciano, ItalyWe 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 <inline-formula> <math display="inline"> <semantics> <mi>&#977;</mi> </semantics> </math> </inline-formula>-methods for Volterra integral equations.https://www.mdpi.com/2075-1680/7/4/91stochastic differential equationsstochastic multistep methodsstochastic Volterra integral equationsmean-square stabilityasymptotic stability
collection DOAJ
language English
format Article
sources DOAJ
author Angelamaria Cardone
Dajana Conte
Raffaele D’Ambrosio
Beatrice Paternoster
spellingShingle Angelamaria Cardone
Dajana Conte
Raffaele D’Ambrosio
Beatrice Paternoster
Stability Issues for Selected Stochastic Evolutionary Problems: A Review
Axioms
stochastic differential equations
stochastic multistep methods
stochastic Volterra integral equations
mean-square stability
asymptotic stability
author_facet Angelamaria Cardone
Dajana Conte
Raffaele D’Ambrosio
Beatrice Paternoster
author_sort Angelamaria Cardone
title Stability Issues for Selected Stochastic Evolutionary Problems: A Review
title_short Stability Issues for Selected Stochastic Evolutionary Problems: A Review
title_full Stability Issues for Selected Stochastic Evolutionary Problems: A Review
title_fullStr Stability Issues for Selected Stochastic Evolutionary Problems: A Review
title_full_unstemmed Stability Issues for Selected Stochastic Evolutionary Problems: A Review
title_sort stability issues for selected stochastic evolutionary problems: a review
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2018-12-01
description 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 <inline-formula> <math display="inline"> <semantics> <mi>&#977;</mi> </semantics> </math> </inline-formula>-methods for Volterra integral equations.
topic stochastic differential equations
stochastic multistep methods
stochastic Volterra integral equations
mean-square stability
asymptotic stability
url https://www.mdpi.com/2075-1680/7/4/91
work_keys_str_mv AT angelamariacardone stabilityissuesforselectedstochasticevolutionaryproblemsareview
AT dajanaconte stabilityissuesforselectedstochasticevolutionaryproblemsareview
AT raffaeledambrosio stabilityissuesforselectedstochasticevolutionaryproblemsareview
AT beatricepaternoster stabilityissuesforselectedstochasticevolutionaryproblemsareview
_version_ 1725268519306657792

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