Exponential stability of first and second order differential evolution equations of Itô type. (Ukrainian, English) Zbl 1240.60154
Mat. Metody Fiz.-Mekh. Polya 52, No. 4, 99-107 (2009); translation in J. Math. Sci., New York 174, No. 2, 243-253 (2011).
The author presents conditions of exponential stability for differential evolution equations obtained in terms of heat conduction equations. In order to determine the stochastic stability domain for solutions to these equations the method of Lyapunov functional construction is used.
Reviewer: A. A. Martynyuk (Kyïv)
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G52 | Stable stochastic processes |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
