African Diaspora Journal of Mathematics

On the Existence of Almost Automorphic Solutions of Nonlinear Stochastic Volterra Difference Equations

P. H. Bezandry

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In this paper, we introduce a concept of almost automorphy for random sequences. Using the Banach contraction principle, we establish the existence and uniqueness of an almost automorphic solution to some Volterra stochastic difference equation in a Banach space. Our main results extend some known ones in the sense of mean almost automorphy. As an application, almost automorphic solution to a concrete stochastic difference equation is analyzed to illustrate our abstract results.

Article information

Afr. Diaspora J. Math. (N.S.) Volume 15, Number 1 (2013), 14-24.

First available in Project Euclid: 9 August 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39A10: Difference equations, additive 60G07: General theory of processes 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

almost automorphic sequence Stochastic Volterra difference equation


Bezandry, P. H. On the Existence of Almost Automorphic Solutions of Nonlinear Stochastic Volterra Difference Equations. Afr. Diaspora J. Math. (N.S.) 15 (2013), no. 1, 14--24.

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  • D. Araya, R.Castro, and C. Lizama, Almost automorphic solutions of difference equations, Adv, Difference Equ., 2009, 15pp
  • P. Bezandry and T. Diagana, Almost periodic stochastic processes, Springer, New York, 2011.
  • P. Bezandry, T. Diagana, and S. Elaydi, On the stochastic Beverton-Holt equation with survival rates, J. Difference Eq. Appl. 14, no. 2 (2008), pp. 175-190.
  • S. Bochner, A new approach to almost automorhy, Proc., Natl. Acad, Sci. USA 48 (1962), 2039-2043.
  • C. Corduneanu, Almost periodic functions, 2nd Edition, Chelsea-New York, 1989.
  • C. Cuevas, H. Henriquez, and C. Lizama, On the existence of almost automorphic solutions of Volterra difference equations, J. Difference Equations and Appl., 10, no. 11 (2012), 1931-1946.
  • T. Diagana, Existence of globally attracting almost automorphic solutions to some nonautonomous higher-order difference equations, Appl. Math. Comput. 219 (2013), 6510-6519.
  • T. Diagana, S. Elaydi, and A-A Yakubu, Population models in almost periodic environments, J. Difference Equations and Appl., 13, no. 4 (2007), 239-260.
  • T. Diagana and G. N'Guereketa, Almost automorphic solutions to semilinear evolution equations, Funct. Differ. Equ. 13 (2006), 195-206.
  • J. Han and C. Hong, Almost periodic random sequences in probability, J. Math. Anal. Appl., 336 (2007), 962-974.
  • J. Hong and C. Nunez, The almost periodic type difference equations, Mathl. Comput. Modeling, Vol. 28, No. 12 (1998), pp. 21-31.
  • G. N'Guerekata, Almost automorphic and almost periodic functions in abstract spaces, Kluwer Academic Plenum Publishers, New York, London, Moscou (2001).
  • G. N'Guerekata, Topics in almost automorphy, Springer, New York, Boston, Dordrecht, London, Moscou, 2005.