Orthogonal Polynomials in the Spectral Analysis of Markov Processes (Hardcover) (ISBN-13: 9781316516553)

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.

Author: Manuel Dom?guez de la Iglesia
ISBN-10: 1316516555
ISBN-13: 9781316516553
Publisher: Cambridge University Press
Language: English
Published: 10/21/2021
Pages: 390
Format: Hardcover
Weight: 1.57lbs
Size: 9.21h x 6.14w x 0.94d