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Orthogonal Polynomials in the Spectral Analysis of Markov Processes : Birth-Death Models and Diffusion.
・ISBN 978-1-316-51655-3 hard GB£ 109.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-03054-0
| 著者・編者 | de la Iglesia, Manuel Dominguez, |
|---|---|
| シリーズ | Encyclopedia of Mathematics and its Applications |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2021 |
| ページ数 | 390 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-9655＞ |
解説
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.