Semilinear stochastic evolution equations: boundedness, stability and invariant measurest
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 12 (1) , 1-39
- https://doi.org/10.1080/17442508408833293
Abstract
Boundedness and stability of the Markov processes associated with a semilinear stochastic evolution equation is studied by the Liapunov method. Sufficient conditions for existence and uniqueness of invariant measures are also given. As preliminaries ihe Feller property relative io the weak topology, Ito's iormuia lor mild solutions and continuity of sample paths are examined. An extension to the local Lipschitz nonlinearities is then discussed For illustration three examples are included.Keywords
This publication has 19 references indexed in Scilit:
- Stability of nonlinear stochastic-evolution equationsJournal of Mathematical Analysis and Applications, 1982
- On the path regularity of a stochastic process in a hilbert space, defined by the ito integralStochastics, 1982
- Markov processes generated by linear stochastic evolution equationsStochastics, 1981
- Stability of stochastic partial differential equationJournal of Mathematical Analysis and Applications, 1981
- Stochastic stability of differential equationsPublished by Springer Nature ,1980
- Dynamic Programming Approach to Stochastic Evolution EquationsSIAM Journal on Control and Optimization, 1979
- Asymptotic stability of the linear ito equation in infinite dimensionsJournal of Mathematical Analysis and Applications, 1978
- Infinite Dimensional Linear Systems TheoryPublished by Springer Nature ,1978
- Ito's lemma in infinite dimensionsJournal of Mathematical Analysis and Applications, 1970
- Markov ProcessesPublished by Springer Nature ,1965