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.
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DOI : 10.1051/ps/2020004
Mots-clés : Continuous-time reversible Markov process, Lancaster probabilities, orthogonal polynomials, spectral expansion
@article{PS_2020__24_1_100_0,
author = {Mena, Rams\'es H. and Palma, Freddy},
title = {Continuous-time {Markov} processes, orthogonal polynomials and {Lancaster} probabilities},
journal = {ESAIM: Probability and Statistics},
pages = {100--112},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2020004},
mrnumber = {4071319},
zbl = {1434.60196},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2020004/}
}
TY - JOUR AU - Mena, Ramsés H. AU - Palma, Freddy TI - Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities JO - ESAIM: Probability and Statistics PY - 2020 SP - 100 EP - 112 VL - 24 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2020004/ DO - 10.1051/ps/2020004 LA - en ID - PS_2020__24_1_100_0 ER -
%0 Journal Article %A Mena, Ramsés H. %A Palma, Freddy %T Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities %J ESAIM: Probability and Statistics %D 2020 %P 100-112 %V 24 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2020004/ %R 10.1051/ps/2020004 %G en %F PS_2020__24_1_100_0
Mena, Ramsés H.; Palma, Freddy. Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 100-112. doi : 10.1051/ps/2020004. http://www.numdam.org/articles/10.1051/ps/2020004/
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