On the Probability of Pattern Matching in Nonaligned DNA Sequences: A Finite Markov Chain Imbedding Approach

1999 ◽  
pp. 287-302 ◽  
Author(s):  
James C. Fu ◽  
W. Y. Wendy Lou ◽  
S. C. Chen
Keyword(s):  
Markov Chain ◽  
Pattern Matching ◽  
Dna Sequences ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding

Waiting times for patterns in a sequence of multistate trials

2001 ◽  
Vol 38 (2) ◽  
pp. 508-518 ◽  
Author(s):  
Demetrios L. Antzoulakos
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Waiting Times ◽  
Random Variable ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Markov Chain Imbedding Method ◽  
Runs And Patterns ◽  
Imbedding Method

Let Xn, n ≥ 1 be a sequence of trials taking values in a given set A, let ∊ be a pattern (simple or compound), and let Xr,∊ 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 Xr,∊ in the case of the non-overlapping and overlapping way of counting runs and patterns. Several extensions and generalizations are also discussed.

Waiting times for patterns in a sequence of multistate trials

2001 ◽  
Vol 38 (02) ◽  
pp. 508-518 ◽  
Author(s):  
Demetrios L. Antzoulakos
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Waiting Times ◽  
Random Variable ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Markov Chain Imbedding Method ◽  
Runs And Patterns ◽  
Imbedding Method

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.

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