On Uniform Stability with Growth Rates of Stochastic Skew-Evolution Semiflows in Banach Spaces

Abstract

The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as particular cases, the concepts of uniform exponential stability in mean and uniform polynomial stability in mean. Extending techniques employed in the deterministic case, we obtain variants of some results for the general cases of uniform stability in mean for stochastic skew-evolution semiflows in Banach spaces.

Keywords

• stochastic skew-evolution semiflows
• stochastic evolution cocycle
• growth rate
• uniform stability in mean