Orthogonal Polynomials in the Spectral Analysis of Markov Processes: Birth-Death Models and Diffusion...

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Manuel Domínguez de la Iglesia (Universidad Nacional Autónoma de México)

Orthogonal Polynomials in the Spectral Analysis of Markov Processes

Birth-Death Models and Diffusion

Manuel Domínguez de la Iglesia (Universidad Nacional Autónoma de México)

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English

Cambridge University Press
21 October 2021

Calculus & mathematical analysis; Stochastics

Series: Encyclopedia of Mathematics and its Applications

In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.

By: Manuel Domínguez de la Iglesia (Universidad Nacional Autónoma de México)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 163mm, Spine: 25mm
Weight: 700g
ISBN: 9781316516553
ISBN 10: 1316516555
Series: Encyclopedia of Mathematics and its Applications
Pages: 390
Publication Date: 21 October 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Manuel Domínguez de la Iglesia is Professor of Mathematics at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.

Reviews for Orthogonal Polynomials in the Spectral Analysis of Markov Processes: Birth-Death Models and Diffusion

'The book serves as an excellent research monograph in this field and is strongly recommended by the reviewer to the researchers working in this field - both statisticians and mathematicians.' Lalit Mohan Upadhyaya, zbMATH Open