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An application of skew product maps to Markov chains

Kowalski Z. S.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 1

35-41

By using the skew product definition of a Markov chain we obtain the following results: (a) Every k-step Markov chain is a quasi-Markovian process. (b) Every piecewise linear map with a Markovian partition defines a Markov chain forevery absolutely continuous invariant measure. (c) Satisfying the Chapman-Kolmogorov equation is not sufficient for a process to be quasi-Markovian.

Skew products of ideals

Fremlin D. H.

Journal of Applied Analysis

2003

Vol. 9, nr 1

1-18

I investigate an asymmetric product construction for σ-ideals of σ-algebras of sets, corresponding to one-sided Fubini and Kuratowski-Ulam theorems, examining the cellularities of these products.