Random Markov processes and uniform martingales. (English) Zbl 0711.60041

Kalikow, Steve

Isr. J. Math. 71, No. 1, 33-54 (1990).

The author introduces complete random Markov processes, which generalize n-step Markov chains and uniform martingales, which are the same as “continuous g-functions” defined in one of the cited references. The first result states that the class of uniform martingales coincides with the class of random Markov processes (the first coordinate of a complete random Markov process). Several properties related to ergodic theory are mentioned, conjectures are discussed and examples are given.

Reviewer: A.Gut

MSC:

60G42	Martingales with discrete parameter
60G10	Stationary stochastic processes
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

complete random Markov processes; uniform martingales; ergodic theory

References:

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