Exactly Solvable Birth and Death Processes
Mathematical Physics
2015-05-13 v1 Statistical Mechanics
High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Probability
Exactly Solvable and Integrable Systems
Data Analysis, Statistics and Probability
Abstract
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' quantum mechanics, which is recently proposed by Odake and the author. The (-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of ( being the population) corresponding to the -Racah polynomial.
Cite
@article{arxiv.0903.3097,
title = {Exactly Solvable Birth and Death Processes},
author = {Ryu Sasaki},
journal= {arXiv preprint arXiv:0903.3097},
year = {2015}
}
Comments
LaTeX, amsmath, amssymb, 24 pages, no figures