Orthogonal Polynomials in the Spectral Analysis of Markov Processes
Birth-Death Models and Diffusion
Part of Encyclopedia of Mathematics and its Applications
- Author: Manuel Domínguez de la Iglesia, Universidad Nacional Autónoma de México
- Date Published: October 2021
- availability: Available
- format: Hardback
- isbn: 9781316516553
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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.
Read more- The first text to bring together all the main results on the spectral representation of the most important one-dimensional Markov processes
- Many detailed examples of the spectral analysis of birth-death models and diffusion processes and the probabilistic consequences
- Accessible to graduate students with a background in probability
Reviews & endorsements
'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
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×Product details
- Date Published: October 2021
- format: Hardback
- isbn: 9781316516553
- length: 390 pages
- dimensions: 240 x 163 x 25 mm
- weight: 0.7kg
- availability: Available
Table of Contents
1. Orthogonal polynomials
2. Spectral representation of discrete-time birth-death chains
3. Spectral representation of birth-death processes
4. Spectral representation of diffusion processes
References
Index.
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