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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2017: 0.71

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2353-0626
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Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

Mark A. McKibben
  • Corresponding author
  • Department of Mathematics, West Chester University, 25 University Avenue, West Chester, PA, 19383, USA
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Micah Webster
  • Center for Data, Mathematical, and Computational Sciences, Goucher College, 1021 Dulaney Valley Road, Baltimore, USA
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-05-17 | DOI: https://doi.org/10.1515/msds-2018-0005

Abstract

This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory.

Keywords: Stochastic evolution equation; fractional Brownian motion; second-order equation; Poisson jumps; cosine family

MSC 2010: 60H05; 60H15; 60H20; 35R09

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About the article

Received: 2017-08-21

Accepted: 2018-04-07

Published Online: 2018-05-17


Citation Information: Nonautonomous Dynamical Systems, Volume 5, Issue 1, Pages 59–75, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2018-0005.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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