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Contemporary Mathematics. Fundamental Directions, 2006, Volume 17, Pages 110–128 (Mi cmfd60)  
This article is cited in 10 scientific papers (total in 10 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 (10)
References:
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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}
Linking options:
  • https://www.mathnet.ru/eng/cmfd60
  • https://www.mathnet.ru/eng/cmfd/v17/p110
    • This publication is cited in the following 10 articles:
    1. Tomás Caraballo, Faten Ezzine, Mohamed Ali Hammami, “Boundedness and Partial Convergence of Solution of a Class of Stochastic Differential Equations”, Qual. Theory Dyn. Syst., 24:2 (2025)  crossref
    2. Liu W., Foondun M., Mao X., “Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations”, Stat. Probab. Lett., 92 (2014), 173–182  crossref  mathscinet  zmath  isi
    3. Rodkina A., Dokuchaev N., “Instability and Stability of Solutions of Systems of Nonlinear Stochastic Difference Equations with Diagonal Noise”, J. Differ. Equ. Appl., 20:5-6, SI (2014), 744–764  crossref  mathscinet  zmath  isi
    4. Alexandra Rodkina, Springer Proceedings in Mathematics & Statistics, 94, Recent Advances in Delay Differential and Difference Equations, 2014, 219  crossref
    5. Berkolaiko G., Kelly C., Rodkina A., “Sharp Pathwise Asymptotic Stability Criteria for Planar Systems of Linear Stochastic Difference Equations”, Discret. Contin. Dyn. Syst., 2011, no. S, SI, 163–173  mathscinet  zmath  isi
    6. Appleby J.A.D., Rodkina A., Schurz H., “Non-positivity and oscillations of solutions of nonlinear stochastic difference equations with state-dependent noise”, J. Difference Equ. Appl., 16:7 (2010), 807–830  crossref  mathscinet  zmath  isi
    7. Kelly C., Rodkina A., “Constrained stability and instability of polynomial difference equations with state-dependent noise”, Discrete Contin. Dyn. Syst. Ser. B, 11:4 (2009), 913–933  crossref  mathscinet  zmath  isi
    8. Appleby J.A.D., Berkolaiko G., Rodkina A., “Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise”, Stochastics, 81:2 (2009), 99–127  mathscinet  zmath  isi
    9. John A.D. Appleby, Gregory Berkolaiko, Alexandra Rodkina, “Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise”, Stochastics, 81:2 (2009), 99  crossref
    10. Appleby J., Berkolaiko G., Rodkina A., “On local stability for a nonlinear difference equation with a non-hyperbolic equilibrium and fading stochastic perturbations”, J. Difference Equ. Appl., 14:9 (2008), 923–951  crossref  mathscinet  zmath  isi
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