This article is cited in 20 papers

Ergodic properties of discrete quadratic stochastic processes defined on von Neumann algebras

N. N. Ganikhodzhaev, F. M. Mukhamedov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: The paper contains necessary and sufficient conditions under which the ergodic principle and the regularity condition hold for discrete quantum quadratic stochastic processes defined on von Neumann algebras. A connection between these processes and Markov processes is established.

MSC: 60G99, 60H99, 60J35, 60K35, 58F11, 60J99, 58F20, 57R50, 92D25, 15A51, 60J35

Received: 21.07.1999

DOI: 10.4213/im302

 English version: Izvestiya: Mathematics, 2000, 64:5, 873–890

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