On A Family of Isospectral Pure-Birth Processes

Abstract

It is shown that every spectrum of a finite irreducible Markov generator whose eigen-values are real and of geometric multiplicity 1 can be obtained as the spectrum of an irreducible pure-birth Markov process with jumps from the right-most boundary to all the other points. A whole isospectral family of such processes is exhibited and their mixing rates are compared.

Reference

Laurent Miclo, and Chi Zhang, “On A Family of Isospectral Pure-Birth Processes”, Alea - Latin American Journal of Probability and Mathematical Statistics, vol. 18, 2021, p. 1759–1771.