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The Asymptotic Behavior of Certain Birth Processes
Siddhartha Sahi
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
sahi@math.rutgers.edu
Annals of Combinatorics 10 (2) p. 255-269 June, 2006
AMS Subject Classification: 60J80, 60J85, 05A19, 33D52
Abstract:
We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance.
Keywords: birth processes, cumulants, Capelli identity, interpolation polynomials, divisors, q¨Cseries

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