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A note on the product of random elements of a semigroup

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Abstract

LetX=(X 0,X 1, ...) be a Markov chain on the discrete semigroupS. X is assumed to have one essential classC such thatC∩K≠ℓ, whereK is the kernel ofS. We study the processY=(Y 0,Y 1,...) whereY n =X 0 X 1 ...X n using the auxiliary process\(Z = \left( {\begin{array}{*{20}c} X \\ Y \\ \end{array} } \right)\) which is a Markov chain onS×S. The essential classes and the limiting distribution of theZ-chain are determined. (These results were obtained earlier byH. Muthsam, Mh. Math.76, 43–54 (1972). However, his proofs contained an error restricting the validity of his results.

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Authors and Affiliations

  1. Aarhus

    Göran Högnäs

  2. Matematiska Institutionen, Åbo Akademi, SF-20500, Åbo 50, Finland

    Göran Högnäs

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  1. Göran Högnäs
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Supported in part by the Danish Ministry of Education and the Toroch Ellida Ljungbergs fond.

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Högnäs, G. A note on the product of random elements of a semigroup. Monatshefte für Mathematik 85, 317–321 (1978). https://doi.org/10.1007/BF01305960

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