Compound Poisson and Poisson process approximations for occurrences of multiple words in Markov chains.
We derive a Poisson process approximation for the occurrences of clumps of multiple words and a compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters generated by a stationary Markov chain. Using the Chen-Stein method, we provide a bound on the error in the approximations. For rare words, these errors tend to zero as the length of the sequence increases to infinity. Modeling a DNA sequence as a stationary Markov chain, we show as an application that the compound Poisson approximation is efficient for the number of occurrences of rare stem-loop motifs.
Department of Statistics, UCLA 90095, USA.
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Reinert
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Schbath
D001483:Base Sequence; D004247:DNA / Q000737:chemistry*; D008390:Markov Chains; D008962:Models, Theoretical; D009690:Nucleic Acid Conformation; D016012:Poisson Distribution
D004247:DNA