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Contents of PMS, Vol. 25, Fasc. 2,
pages 211 - 221
 

CRITERIONS OF THE SIMILARITY FOR RANDOM WALKS AND BIRTH-AND-DEATH PROCESSES

Anna Poskrobko

Abstract: This paper is devoted to study the similarity of birth-and-death processes with a discrete and continuous time. We discuss some relations between the measures of orthogonality of the associated polynomials and the first return probabilities of two a -similar random walks and two n -similar birth-and-death processes. We give the necessary and sufficient conditions for a -similarity of two random walks both in terms of the corresponding spectral measures. We consider analogous conditions for n -similarity of two birth-and-death processes.

2000 AMS Mathematics Subject Classification: Primary 60J80; Secondary 42C05.

Key words and phrases: Associated polynomials, measures of orthogonality, similar random walks, similar birth-and-death processes, first return probabilities.

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