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Contemporary Mathematics. Fundamental Directions, 2006, Volume 17, Pages 110–128 (Mi cmfd60)  

This article is cited in 9 scientific papers (total in 9 papers)

Almost sure polynomial asymptotic stability of stochastic difference equations

J. Applebya, D. Mackeyb, A. Rodkinac

a Dublin City University
b Dublin Institute of Technology
c University of the West Indies
Full-text PDF (284 kB) Citations (9)
References:
Abstract: In this paper, we establish the almost sure asymptotic stability and decay results for solutions of an autonomous scalar difference equation with a nonhyperbolic equilibrium at the origin, which is perturbed by a random term with a fading state–independent intensity. In particular, we show that if the unbounded noise has tails which fade more quickly than polynomially, then the state–independent perturbation dies away at a sufficiently fast polynomial rate in time, and if the autonomous difference equation has a polynomial nonlinearity at the origin, then the almost sure polynomial rate of decay of solutions can be determined exactly.
English version:
Journal of Mathematical Sciences, 2008, Volume 149, Issue 6, Pages 1629–1647
DOI: https://doi.org/10.1007/s10958-008-0086-0
Bibliographic databases:
UDC: 517.55+517.95
Language: Russian
Citation: J. Appleby, D. Mackey, A. Rodkina, “Almost sure polynomial asymptotic stability of stochastic difference equations”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, CMFD, 17, PFUR, M., 2006, 110–128; Journal of Mathematical Sciences, 149:6 (2008), 1629–1647
Citation in format AMSBIB
\Bibitem{AppMacRod06}
\by J.~Appleby, D.~Mackey, A.~Rodkina
\paper Almost sure polynomial asymptotic stability of stochastic difference equations
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~3
\serial CMFD
\yr 2006
\vol 17
\pages 110--128
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd60}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336462}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 6
\pages 1629--1647
\crossref{https://doi.org/10.1007/s10958-008-0086-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40549096004}
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  • https://www.mathnet.ru/eng/cmfd/v17/p110
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Современная математика. Фундаментальные направления
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    Abstract page:462
    Full-text PDF :149
    References:46
     
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