Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes



The aim of this note is to provide an original proof and derive fine properties of the excessive function that characterizes the Laplace transform of the downward first hitting time to a fixed level of a non-degenerate continuous-time branching process. It hinges on a recent result by Choi and Patie (2016) on the potential theory of skip-free Markov chains and reveals, in particular, that the fundamental excessive function that characterizes the first hitting time is a purely excessive function.


Branching processes First passage time Purely excessive function 

Mathematics Subject Classification 2010

60J80 60J45 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et leurs applications, UMR CNRS 5142Université de Pau et des Pays de l’AdourPauFrance
  2. 2.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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