Applications of an operator stochastic integral in Prigogine's theory of irreversible dynamical systems (Q911160)

The subject of this paper is a stochastic approach to the Prigogine theory of irreversible dynamical systems. The basic idea of this theory is that for some dynamical systems described by a unitary group one can find an invertible and positive operator \(\Lambda\) which converts this group into a strict contraction semigroup of a Markov process. In the present paper, the construction of the operator \(\Lambda\) is done by using a stochastic integral technique for dynamical systems which are K- flows. It is also shown that the transformed by \(\Lambda\) semigroup is asymptotically stable. Later, in the authors' paper, Physica A 166, 220-228 (1990), it was shown that the assumption on a dynamical system that it is a K-flow is not only sufficient but also necessary.