African Diaspora Journal of Mathematics

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

P. H. Bezandry

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
http://projecteuclid.org/euclid.adjm/1376053757

Mathematical Reviews number (MathSciNet)
MR3091707

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

Keywords
almost automorphic sequence Stochastic Volterra difference equation

Citation

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. http://projecteuclid.org/euclid.adjm/1376053757.


Export citation

References

  • 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.