Waiting times for patterns in a sequence of multistate trials

Let X n , n ≥ 1 be a sequence of trials taking values in a given set A, let ∊ be a pattern (simple or compound), and let X r,∊ be a random variable denoting the waiting time for the rth occurrence of ∊. In the present article a finite Markov chain imbedding method is developed for the study of X r,∊...

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Bibliographic Details
Published in:Journal of applied probability 2001-06, Vol.38 (2), p.508-518
Main Author: Antzoulakos, Demetrios L.
Format: Article
Language:English
Subjects:
60E05
60J10
Distribution theory
Embedded systems
Embeddings
Exact sciences and technology
Experimentation
Generating function
Markov analysis
Markov chain
Markov chains
Markov processes
Mathematical sequences
Mathematical vectors
Mathematics
Matrices
multistate trials
pattern
Probability and statistics
Probability theory and stochastic processes
Random variables
Reliability
Research Papers
Sciences and techniques of general use
sooner and later waiting time problems
Studies
Transition probabilities
waiting time distribution
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Summary:Let X n , n ≥ 1 be a sequence of trials taking values in a given set A, let ∊ be a pattern (simple or compound), and let X r,∊ be a random variable denoting the waiting time for the rth occurrence of ∊. In the present article a finite Markov chain imbedding method is developed for the study of X r,∊ in the case of the non-overlapping and overlapping way of counting runs and patterns. Several extensions and generalizations are also discussed.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/996986759