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.
| ISBN: | 9781316516553 |
| Publication date: | 21st October 2021 |
| Author: | Manuel Domínguez Universidad Nacional Autónoma de México de la Iglesia |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 390 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Calculus and mathematical analysis Stochastics |
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.
Orthogonal Polynomials in the Spectral Analysis of Markov Processes features in the following genres: Calculus and mathematical analysis, Stochastics
Orthogonal Polynomials in the Spectral Analysis of Markov Processes is available in Hardback
Orthogonal Polynomials in the Spectral Analysis of Markov Processes was written by Manuel Domínguez Universidad Nacional Autónoma de México de la Iglesia and published by Cambridge University Press
Orthogonal Polynomials in the Spectral Analysis of Markov Processes has 390 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series
£98.10