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© Oxford University Press

First and second moment of counts of words in random texts generated by Markov chains

J. Kleffe and M. Borodovsky 1

Institute of Molecular Biology and Biochemistry, Department of Molecular Biology and Informatics, Free University of Berlin Arnimallee 22, D-1000, Berlin 33, Germany
1School of Biology, Georgia Institute of Technology Atlanta, GA 30332, USA and Institute of Molecular Genetics 123182 Moscow

An exact expression for the variance of random frequency that a given word has in text generated by a Markov chain is presented. The result is applied to periodic Markov chains, which describe the protein-coding DNA sequences better than simple Markov chains. A new solution to the problem of word overlap is proposed. It was found that the expected frequency and overlapping properties determine most of the variance. The expectation and variance of counts for triplets are compared with experimental counts in Escherichia coli coding sequences.

Received on June 11, 1991; accepted on January 31, 1992

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