Sample Path Behaviors of Lévy Processes Conditioned to Avoid Zero

Abstract

Takeda and Yano (Electron J Probab 28:1–35, 2023) determined the limit of Lévy processes conditioned to avoid zero via various random clocks in terms of Doob’s \(h\)-transform, where the limit processes may differ according to the choice of random clocks. The purpose of this paper is to investigate sample path behaviors of the limit processes in long time and in short time.