TY  - JOUR
ID  - Hai2025
LB  - Hai2025
AU  - Hai, Pham Viet
TI  - Datko-type theorems concerning asymptotic behaviour of exponential type in mean
ST  - Datko-type theorems concerning asymptotic behaviour of exponential type in mean
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 4
SP  - 451
EP  - 470
DO  - https://doi.org/10.7494/OpMath.2025.45.4.451
UR  - https://doi.org/10.7494/OpMath.2025.45.4.451
AB  - 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.
KW  - exponential stability
KW  - exponential instability
KW  - stochastic skew-evolution semiflows
KW  - Datko's theorem
KW  - Banach function spaces
SN  - 1232-9274
ER  -