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.

Gathers all the main results on the spectral representation of one-dimensional Markov processes, with examples and applications.

About the Author
Manuel Dominguez de la Iglesia is Professor of Mathematics at the Instituto de Matematicas of the Universidad Nacional Autonoma de Mexico.

Reviews
'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



Book Information
ISBN 9781316516553
Author Manuel Dominguez de la Iglesia
Format Hardback
Page Count 390
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 700g
Dimensions(mm) 240mm * 163mm * 25mm