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Square-mean pseudo almost automorphic process and its application to stochastic evolution equations. (English) Zbl 1233.60030

The authors originate a stochastic version of the theory of almost almost automorphy. At first, definitions of abstract spaces and square-mean pseudo almost automorphic processes are introduced. Some results not only on the completeness of the space of square-mean pseudo almost automorphic processes but also on the composition of such processes are included. Then, based on these results, existence as well as uniqueness of square-mean pseudo almost automorphic solutions to linear stochastic evolution equations are proved. Several theorems are established concerning the global stability of square-mean pseudo almost automorphic solutions to linear SEEs. Finally, an example is provided to show the feasibility of the developed theoretical results.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
60H30 Applications of stochastic analysis (to PDEs, etc.)
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