Volume 24, 2020
|Page(s)||100 - 112|
|Published online||03 March 2020|
Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities
Department of Probability and Statistics, IIMAS, UNAM,
Mexico city, Mexico.
* Corresponding author: email@example.com
Accepted: 15 January 2020
This work links the conditional probability structure of Lancaster probabilities to a construction of reversible continuous-time Markov processes. Such a task is achieved by using the spectral expansion of the corresponding transition probabilities in order to introduce a continuous time dependence in the orthogonal representation inherent to Lancaster probabilities. This relationship provides a novel methodology to build continuous-time Markov processes via Lancaster probabilities. Particular cases of well-known models are seen to fall within this approach. As a byproduct, it also unveils new identities associated to well known orthogonal polynomials.
Mathematics Subject Classification: 60J25 / 60J35 / 33C45
Key words: Continuous-time reversible Markov process / Lancaster probabilities / orthogonal polynomials / spectral expansion
© EDP Sciences, SMAI 2020
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