Orthogonal Polynomials in the Spectral Analysis of Markov Processes: Birth-Death Models and Diffusion (Encyclopedia of Mathematics and its Applications, Series Number 181)

"In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing the 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 all 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"-- Provided by publisher. This book gathers all the main results on the spectral representation of the most important one-dimensional Markov processes, with examples and applications. Covering sixty years of research, it is an essential resource for graduate students and researchers interested in the connection between orthogonal polynomials and stochastic processes. Frontmatter Dedication Contents Preface Spectral_Representation_of_Discrete-Time_BirthDeath_Chains Small_Phenomena_Big_Implications Spectral_Representation_of_BirthDeath_Processes Spectral_Representation_of_Diffusion_Processes References ndex