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

2020/01/07 by Clément Foucart, Foucart, Clément, Pei-Sen Li +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2001.02195

openalex publication_date 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 O. Kallenberg 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.

Citations

• Entrance and exit at infinity for stable jump diffusions

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