Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations

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

来源：Nonlinear Analysis: Real World Applications , 2011, 12(2): 1130-1139.

DOI：10.1016/j.nonrwa.2010.09.007

• Stepanov-like almost automorphy
• Square-mean almost automorphy
• Stochastic differential equations

In this paper, we introduce a new concept of Stepanov-like almost automorphy (or S(2)-almost automorphy) for stochastic processes. We use the results obtained to investigate the existence and uniqueness of a Stepanov-like almost automorphic mild solution to a class of nonlinear stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean almost automorphy.

• 出版日期2011-4
• 单位兰州交通大学; 西北师范大学