this paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable hilbert space. themain technique is based upon an appropriate composition theorem combined with the banachcontraction mapping principle and an analytic semigroup of linear operators.

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

The paper studies the notion of Stepanov almost periodicity (or S-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 e...

Our work is concerned with a neural network with n nodes, where the activity of the k-th cell depends on external, stochastic inputs as well as the coupling generated by the activity of the adjacent cells, transmitted through a diffusion process in the network. This paper aims to throw some light on time-varying, stochastically perturbed, neuronal networks. We show that when the coefficients os...