Existence of $S^2$-almost periodic solutions to a class of nonautonomous stochastic evolution equations

P. Bezandry, Howard University, Washington, DC, U.S.A.
T. Diagana, Howard University, Washington, DC, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 35. (2008), pp. 1-19.

Abstract: The paper studies the notion of Stepanov almost periodicity (or $S^2$-almost periodicity) for stochastic processes, which is weaker than the notion of quadratic-mean almost periodicity. Next, we make extensive use of the so-called Acquistapace and Terreni conditions to prove the existence and uniqueness of a Stepanov (quadratic-mean) almost periodic solution to a class of nonautonomous stochastic evolution equations on a separable real Hilbert space. Our abstract results will then be applied to study Stepanov (quadratic-mean) almost periodic solutions to a class of $n$-dimensional stochastic parabolic partial differential equations.

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