A new composition theorem for square-mean almost automorphic functions and applications to stochastic differential equations

作者：Chang Yong Kui^*; Zhao Zhi Han; N'Guerekata G M

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(6): 2210-2219.

DOI：10.1016/j.na.2010.11.025

• Composition theorem of square-mean almost automorphic functions
• Stochastic differential equations
• Schauder's fixed point theorem

In this paper, we establish a new composition theorem for square-mean almost automorphic functions under conditions which are different from Lipschitz conditions in the literature. We apply this new composition theorem together with Schauder's fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions for a stochastic differential equation in a real separable Hilbert space. Finally, an interesting corollary is also given for the sub-linear growth cases.

• 出版日期2011-3-15
• 单位西北师范大学; 兰州交通大学