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 random 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

† Research supported by TMR grant ERBFMBICT950067 of the European Community.