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Potential Analysis

, Volume 42, Issue 2, pp 585–605 | Cite as

New Results on Hunt’s Hypothesis (H) for Lévy Processes

  • Ze-Chun Hu
  • Wei Sun
  • Jing Zhang
Article

Abstract

In this paper, we present new results on Hunt’s hypothesis (H) for Lévy processes. We start with a comparison result on Lévy processes which implies that big jumps have no effect on the validity of (H). Based on this result and the Kanda-Forst-Rao theorem, we give examples of subordinators satisfying (H). Afterwards we give a new necessary and sufficient condition for (H) and obtain an extended Kanda-Forst-Rao theorem. By virtue of this theorem, we give a new class of Lévy processes satisfying (H). Finally, we construct a type of subordinators that does not satisfy Rao’s condition.

Keywords

Hunt’s hypothesis (H) Getoor’s conjecture Lévy process Subordinator 

Mathematics Subject Classifications (2010)

Primary: 60J45 Secondary: 60G51 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

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