Stepanov-like weighted asymptotic behavior of solutions to some stochastic differential equations in Hilbert spaces

作者：Tang Chao; Chang Yong Kui^*

来源：APPLICABLE ANALYSIS, 2014, 93(12): 2625-2646.

DOI：10.1080/00036811.2014.880780

• Stepanov-like weighted pseudo almost automorphy for stochastic processes
• square-mean weighted pseudo almost automorphy for stochastic processes
• stochastic differential equations
• 34D23
• 60H30
• 34F05
• 34C27

In this paper, we first introduce the notation and properties of -weighted pseudo almost automorphy for stochastic processes. And then, we apply the results obtained to consider the existence and uniqueness of -weighted pseudo almost automorphic solutions to some stochastic differential equations in a real separable Hilbert space under global Lipschitz conditions. Moreover, we also investigate asymptotic behavior of solutions to a stochastic differential equation under -weighted pseudo almost automorphic coefficients without global Lipschitz conditions. Our main results extend some known ones in the sense of square-mean weighted pseudo almost automorphy or -pseudo almost automorphy for stochastic processes.

• 出版日期2014-12-2
• 单位兰州交通大学