Orthogonal polynomials in the spectral analysis of Markov processes : birth-death models and diffusion / Manuel Domínguez de la Iglesia.

Format:

Book

Author/Creator:

Iglesia, Manuel Domínguez de la, author.

Series:

Encyclopedia of mathematics and its applications ; 181.

Encyclopedia of mathematics and its applications ; 181

Language:

English

Subjects (All):

Birth and death processes (Stochastic processes).

Spectral theory (Mathematics).

Orthogonal polynomials.

Physical Description:

1 online resource (xii, 334 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2022.

Summary:

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.

Contents:

Orthogonal polynomials

Spectral representation of discrete-time birth-death chains

Spectral representation of birth-death processes

Spectral representation of diffusion processes.

Notes:

Title from publisher's bibliographic system (viewed on 11 Oct 2021).

Includes bibliographical references and index.

Other Format:

Print version:

ISBN:

9781009035200

1009035207

9781009030540

100903054X

OCLC:

1481801370