Compound Poisson approximations for word patterns under Markovian hypotheses
- 1 December 1995
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 32 (4) , 877-892
- https://doi.org/10.2307/3215201
Abstract
Consider a stationary Markov chain with state space consisting of the ξ -letter alphabet set Λ= {a1, a2, ···, aξ }. We study the variables M=M(n, k) and N=N(n, k), defined, respectively, as the number of overlapping and non-overlapping occurrences of a fixed periodic k-letter word, and use the Stein–Chen method to obtain compound Poisson approximations for their distribution.Keywords
This publication has 18 references indexed in Scilit:
- Stein's Method for Compound Poisson Approximation: The Local ApproachThe Annals of Applied Probability, 1994
- Improved Poisson approximations for word patternsAdvances in Applied Probability, 1993
- Poisson approximations for runs and patterns of rare eventsAdvances in Applied Probability, 1991
- Two Moments Suffice for Poisson Approximations: The Chen-Stein MethodThe Annals of Probability, 1989
- A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trialsProbability Theory and Related Fields, 1988
- Some Poisson Approximations Using CompensatorsThe Annals of Probability, 1983
- Ordered thinnings of point processes and random measuresStochastic Processes and their Applications, 1983
- On the limit of the Markov binomial distributionJournal of Applied Probability, 1981
- Dependent thinning of point processesJournal of Applied Probability, 1980
- A General Poisson Approximation TheoremThe Annals of Probability, 1975