On probability distributions of solutions of semilinear stochastic evolution equations. (English) Zbl 0792.60058

Maslowski, Bohdan

Stochastics Stochastics Rep. 45, No. 1-2, 17-44 (1993).

Author’s summary: Basic properties of transition probability functions of Markov processes corresponding to solutions of semilinear stochastic evolution equations with a general Gaussian noise are studied. Conditions guaranteeing the strong Feller property, irreducibility, the strong law of large numbers and asymptotic stability are given. A Girsanov type theorem is proved.

Reviewer: T.C.Gard (Athens / Georgia)

MSC:

60H15

Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

stochastic evolution equations; strong Feller property; strong law of large numbers; asymptotic stability; Girsanov type theorem