**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.

Communicated by S. K. Ntouyas. | Received on 2008-08-10 Appeared on 2008-11-05 |

**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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