We analyze sequences of letters on a ring. Our objective is to determine the statistics of the occurrences of a set of r-letter words when the sequence is chosen as a periodic Markov chain of order ≤ r - 1. We first obtain a generating function for the associated probability distribution and then display its Poisson limit. For an i.i.d. letter sequence, correction terms to the Poisson limit are given. Finally, we indicate how a hidden Markov chain fits into this scheme.
|Original language||English (US)|
|Number of pages||16|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Jan 2006|
ASJC Scopus subject areas
- Applied Mathematics