An approach to evolution cocycles from a stochastic point of view.

The aim of this paper is to emphasize some splitting asymptotic behaviours in mean square for stochastic cocycles, as well as connections between them. We define a general framework for the exponential splitting that includes, as a particular case, the exponential dichotomy. We will consider general splitting properties that consist in assuming the existence of a decomposition of the state space into invariant subspaces where the norms of the evolution trajectories are bounded by some functions that depend on the initial and final times. The additional conditions target the families of projections. [ABSTRACT FROM AUTHOR]