Structural properties and limit behaviour of linear stochastic systems in Hilbert spaces. (English) Zbl 0573.93076

Mathematical control theory, Banach Cent. Publ. 14, 591-609 (1985).
[For the entire collection see Zbl 0568.00025.]
The structural and asymptotic behaviour of a class of Markov processes on a Hilbert space H are studied. The class is the solution x(t) of the stochastic evolution equation \(dx=Axdt+Bdw\); \(x(0)=x_ 0\in H\), where A is the infinitesimal generator of a \(C_ 0\)-semigroup on H, w is a Wiener process with values in a Hilbert space U and \(B\in L(U,H)\). Properties concerning degeneracy smoothness of the transition probabilities and stationary measures are investigated.
Reviewer: R.Curtain


93E15 Stochastic stability in control theory
60J25 Continuous-time Markov processes on general state spaces
93C05 Linear systems in control theory
46C99 Inner product spaces and their generalizations, Hilbert spaces
60H25 Random operators and equations (aspects of stochastic analysis)
93C25 Control/observation systems in abstract spaces
47D03 Groups and semigroups of linear operators
93B05 Controllability
93E20 Optimal stochastic control


Zbl 0568.00025