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Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence

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  • G. Nuel

    (Sorbonne University)

Abstract

We focus here on the distribution of the random count N of a regular expression in a multi-state random sequence generated by a heterogenous Markov source. We first briefly recall how classical Markov chain embedding techniques allow reducing the problem to the count of specific transitions in a (heterogenous) order 1 Markov chain over a deterministic finite automaton state space. From this result we derive the expression of both the mgf/pgf of N as well as the factorial and non-factorial moments of N. We then introduce the notion of evidence-based constraints in this context. Following the classical forward/backward algorithm in hidden Markov models, we provide explicit recursions allowing to compute the mgf/pgf of N under the evidence constraint. All the results presented are illustrated with a toy example.

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  • G. Nuel, 2019. "Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 875-887, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-019-09700-0
    DOI: 10.1007/s11009-019-09700-0
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    Cited by:

    1. He Yi & Lirong Cui & Narayanaswamy Balakrishnan, 2022. "On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1849-1875, September.

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