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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.