Stochastic Processes and Orthogonal Polynomials

Springer Science & Business Media, 6 déc. 2012 - 184 pages
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The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and diffusions, martingale relations for Lévy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis. Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium.

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Table des matières

The Askey Scheme of Orthogonal Polynomials
Stochastic Processes
Birth and Death Processes Random Walks and Orthogo
Sheffer Systems
Orthogonal Polynomials in Stochastic Integration Theory
Stein Approximation and Orthogonal Polynomials
Conclusion 123
Table of Duality Relations Between Classical Orthogonal
Index 159
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