On the entrance at infinity of Feller processes with no negative jumps

Clément Foucart, Pei-Sen Li and Xiaowen Zhou

Statistics & Probability Letters, 2020, vol. 165, issue C

Abstract: Consider a non-explosive positive Feller process with no negative jumps. It is shown in this note that when infinity is an entrance boundary, in the sense that the entrance times of the process remain bounded when the initial value tends to infinity, the process admits a Feller extension on the compactified state space [0,∞]. Moreover, when started from infinity, the extended Markov process on [0,∞] leaves infinity instantaneously and stays finite, almost-surely. Arguments are adapted from a proof given by Kallenberg (2002) for diffusions. We also show that the process started from x converges weakly towards that started from infinity in the Skorokhod space, when x goes to infinity.

Keywords: Coming down from infinity; Entrance boundary; Feller property; Weak convergence (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108859

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