On associated polynomials and decay rates for birth–death processes

• Published in: Journal of mathematical analysis and applications Vol. 278; no. 2; pp. 500 - 511
• Main Author: van Doorn, Erik A.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.02.2003; Elsevier
• Subjects: Associated polynomials; Birth–death process; Decay rate; Exact sciences and technology; First-entrance time; Markov processes; Mathematical analysis; Mathematics; Numerator polynomials; Orthogonal polynomials; Probability and statistics; Probability theory and stochastic processes; Rate of convergence; Sciences and techniques of general use; Special functions; Associated polynomials; Decay rate; Orthogonal polynomials; Rate of convergence; Numerator polynomials; First-entrance time; Birth–death process; Birth death process; First entrance time; Mathematical analysis; Recurrence relation; Associated polynomial; Numerator polynomial; Convergence rate; Orthogonal polynomial
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/S0022-247X(02)00663-7

We consider sequences of orthogonal polynomials and pursue the question of how (partial) knowledge of the orthogonalizing measure for the associated polynomials can lead to information about the orthogonalizing measure for the original polynomials. In particular, we relate the supports of the two measures, and their moments. As an application, we analyze the relation between two decay rates connected with a birth–death process.