Stochastic Processes and Orthogonal Polynomials

The book offers an accessible reference for researchers in the probabi lity, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of st ochastic processes and orthogonal polynomials. It covers topics like t ime dependent and asymptotic analysis for birth-death processes and di vy processes, stochastic integral s and Stein's approximation method. Almost all well-known orthogonal p olynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathemati cal role of orthogonal polynomials in the analysis of stochastic proce sses and is made accessible for all mathematicians with a basic backgr ound in probability theory and mathematical analysis.