Abstract and Applied Analysis

Almost Automorphic Random Functions in Probability

Hui-Sheng Ding, Chao Deng, and Gaston M. N’Guérékata

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Abstract

We introduce the notion of almost automorphic random functions in probability. Some basic and fundamental properties of such functions are established.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 243748, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276974

Digital Object Identifier
doi:10.1155/2014/243748

Mathematical Reviews number (MathSciNet)
MR3208522

Zentralblatt MATH identifier
07021987

Citation

Ding, Hui-Sheng; Deng, Chao; N’Guérékata, Gaston M. Almost Automorphic Random Functions in Probability. Abstr. Appl. Anal. 2014 (2014), Article ID 243748, 6 pages. doi:10.1155/2014/243748. https://projecteuclid.org/euclid.aaa/1412276974


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References

  • O. Onicescu and V. I. Istrătescu, “Approximation theorems for random functions,” Rendiconti di Matematica, vol. 8, pp. 65–81, 1975.
  • Gh. Cenuşă and I. Săcuiu, “Some properties of random functions almost periodic in probability,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 25, no. 9, pp. 1317–1325, 1980.
  • C. Corduneanu, Almost Periodic Functions, Chelsea, New York, NY, USA, 2nd edition, 1989.
  • C. Deng and H. S. Ding, “Vector valued almost periodic random functionsin čommentComment on ref. [7?]: Please update the information of this reference, if possible.probability,” Journal of Nonlinear Evolution Equations and Applications. In press.
  • Y. Han and J. Hong, “Almost periodic random sequences in probability,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 962–974, 2007.
  • Z.-M. Zheng, H.-S. Ding, and G. M. N'Guérékata, “The space of continuous periodic functions is a set of first category in $AP(X)$,” Journal of Function Spaces and Applications, vol. 2013, Article ID 275702, 3 pages, 2013.
  • G. M. N'Guerekata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic, New York, NY, USA, 2001.
  • G. M. N'Guérékata, Topics in Almost Automorphy, Springer, New York, NY, USA, 2005.
  • P. H. Bezandry and T. Diagana, Almost Periodic Stochastic Processes, Springer, New York, NY, USA, 2011.
  • M. Fu and Z. Liu, “Square-mean almost automorphic solutions for some stochastic differential equations,” Proceedings of the American Mathematical Society, vol. 138, no. 10, pp. 3689–3701, 2010.
  • Z. Chen and W. Lin, “Square-mean pseudo almost automorphic process and its application to stochastic evolution equations,” Journal of Functional Analysis, vol. 261, no. 1, pp. 69–89, 2011.
  • M. Fu and F. Chen, “Almost automorphic solutions for some stochastic differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 80, pp. 66–75, 2013.
  • P. Bezandry and T. Diagana, “Square-mean almost periodic solutions to some classes of nonautonomous stochastic evolution equations with finite delay,” Journal of Applied Functional Analysis, vol. 7, no. 4, pp. 345–366, 2012.
  • Y.-K. Chang, R. Ma, and Z.-H. Zhao, “Almost periodic solutions to a stochastic differential equation in Hilbert spaces,” Results in Mathematics, vol. 63, no. 1-2, pp. 435–449, 2013.
  • H. Zhou, Z. Zhou, and Z. Qiao, “Mean-square almost periodic solution for impulsive stochastic Nicholson's blowflies model with delays,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 5943–5948, 2013. \endinput