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ANALYSIS OF RANDOM WALKS USING ORTHOGONAL POLYNOMIALS
 

Summary: ANALYSIS OF RANDOM WALKS USING
ORTHOGONAL POLYNOMIALS
Erik A. van Doorn* and Pauline Schrijner**
*Faculty of Applied Mathematics, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands
e.a.vandoorn@math.utwente.nl
**Department of Mathematical Sciences, University of Durham
Science Laboratories, South Road, Durham, DH1 3LE, UK
pauline.schrijner@durham.ac.uk
Abstract: We discuss some aspects of discrete-time birth-death processes or ran-
dom walks, highlighting the role played by orthogonal polynomials.
Keywords and phrases: birth-death process, first passage time, quasi-stationary
distribution, random walk, random-walk polynomials, random-walk measure
1991 Mathematics Subject Classification: Primary 60 J 80, Secondary 42 C 05,
60 J 10
1 Introduction
Orthogonal polynomials play an important role in the analysis of Markov chains
(in continuous or discrete time) which are characterized by the fact that direct
transitions can occur only between neighbouring states. In particular, Karlin
and McGregor ([11], [12] and [17]) showed, in the fifties, that the transition

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering