Polynomial behavior in mean of stochastic skew-evolution semiflows

In this paper, we are interested in the more general concept of a polynomial (in)stability in mean in which the polynomial behaviour in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes the classical concepts of a polynomial (in)stability as particular cases. Extending techniques employed in the deterministic case, we obtain variants of a well-known theorem of Datko for a polynomial (in)stability in mean. This is done by using the techniques of stochastic skew-evolution semiflows and Banach spaces of functions or sequences.