Square-mean almost automorphic solutions for some stochastic differential equations
By M. Fu, Zhenxin Liu. 2010
125 citations recorded by the source corpus.
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the coefficients satisfy some conditions. The asymptotic stability of the unique square-mean almost automorphic solution in the square-mean sense is discussed.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/2a33008eb4a96fb0fe23536ec0ab8ab4d085415b
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In Applied Mathematics
- Rathinasamy Sakthivel
- Nazim Idrisoglu Mahmudov
- P. Revathi
- Wei Lin
- Zhenxin Liu
- Zhang Chen
- Jerzy Klamka
- Yuanguo Zhu
In Computational Theory and Mathematics
- Rathinasamy Sakthivel
- P. Revathi
- Wei Lin
- Nazim Idrisoglu Mahmudov
- Zhenxin Liu
- Zhang Chen
- Jerzy Klamka
In Control and Systems Engineering
- Rathinasamy Sakthivel
- Nazim Idrisoglu Mahmudov
- P. Revathi
- Wei Lin
- Zhang Chen
- D. Cheban
- Jerzy Klamka
- J. J. Nieto
Citations in the corpus
- Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations (2017, background): “[26, 27, 32, 34, 40] for periodic equations, [1, 4, 27, 31, 33, 39, 50, 51] for Bohr almost periodic equations and [25, 30, 38, 53] for Bochner almost automorphic equations, and references therein.”
- Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays (2013, background): “[10] T. Caraballo and K. Liu, “Exponential stability of mild solutions of stochastic partial differential equations with delays,” Stochastic Analysis and Applications, vol. 17, no. 5, pp. 743–763, 1999.”
- Square-mean pseudo almost automorphic process and its application to stochastic evolution equations (2011, background): “More recently, in [14], the square-mean almost automorphic process was introduced, and the square-mean almost automorphic mild solution for the stochastic differential equations was investigated, which further generalized the almost automorphic theory from the deterministic version to the stochastic”
- Almost automorphic solutions of dynamic equations on time scales (2013, unknown): “See, [14], [15], [16], [17], [20], [29], [30], [43], for instance and the references therein.”