## Abstract and Applied Analysis

### Almost Automorphic Random Functions in Probability

#### 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

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

#### 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