Abstract
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.
Key words and phrases Chen-Stein method, stem-loop motifs, compound Poisson approximation, Poisson process approximation, occurrences of multiple words.