Abstract
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.
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The second author acknowledges the supports of NSF Grant DMS-1406599 and ARC IAPAS, a fund of the Communautee francaise de Belgique.
The authors are grateful to an anonymous referee for the careful reading of the manuscript.
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Avram, F., Patie, P. & Wang, J. Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes. Methodol Comput Appl Probab 21, 391–399 (2019). https://doi.org/10.1007/s11009-018-9616-5
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DOI: https://doi.org/10.1007/s11009-018-9616-5