Application of Stieltjes theory for S-fractions to birth and death processes

Author:

Bordes G.,Roehner B.

Abstract

We are interested in obtaining bounds for the spectrum of the infinite Jacobi matrix of a birth and death process or of any process (with nearest-neighbour interactions) defined by a similar Jacobi matrix.To this aim we use some results of Stieltjes theory for S-fractions, after reviewing them. We prove a general theorem giving a lower bound of the spectrum. The theorem also gives sufficient conditions for the spectrum to be discrete.The expression for the lower bound is then worked out explicitly for several, fairly general, classes of birth and death processes. A conjecture about the asymptotic behavior of a special class of birth and death processes is presented.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Cited by 21 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Computational methods for birth‐death processes;WIREs Computational Statistics;2018-01-02

2. Spectral properties of birth–death polynomials;Journal of Computational and Applied Mathematics;2015-08

3. Estimation for General Birth-Death Processes;Journal of the American Statistical Association;2014-04-03

4. Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution;Journal of Mathematical Biology;2011-10-09

5. Excursions of diffusion processes and continued fractions;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2011-08-01

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