Opuscula Math. 45, no. 4 (2025), 451-470
https://doi.org/10.7494/OpMath.2025.45.4.451
Opuscula Mathematica
Datko-type theorems concerning asymptotic behaviour of exponential type in mean
Abstract. In this paper, we study the concept of exponential (in)stability in mean for stochastic skew-evolution semiflows, in which the exponential (in)stability in the classical sense is replaced by an average with respect to a probability measure. Our paper consists of three major results. The first is to obtain Datko-type characterizations for the exponential stability in mean of stochastic skew-evolution semiflows. Next, we acquire Datko-type characterizations for the exponential instability in mean by extending the stability techniques. The last is to extend Lyapunov-type equations to the case of exponential (in)stability in mean.
Keywords: exponential stability, exponential instability, stochastic skew-evolution semiflows, Datko's theorem, Banach function spaces.
Mathematics Subject Classification: 93E15, 34D05, 46E30.
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- Pham Viet Hai
https://orcid.org/0000-0001-9993-4070- Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam
- Communicated by P.A. Cojuhari.
- Received: 2025-05-20.
- Accepted: 2025-06-21.
- Published online: 2025-07-16.
