Hunt’s hypothesis (H) and Getoor’s conjecture for Lévy processes

Ze-Chun Hu and Wei Sun

Stochastic Processes and their Applications, 2012, vol. 122, issue 6, 2319-2328

Abstract: In this paper, Hunt’s hypothesis (H) and Getoor’s conjecture for Lévy processes are revisited. Let X be a Lévy process on Rn with Lévy–Khintchine exponent (a,A,μ). First, we show that if A is non-degenerate then X satisfies (H). Second, under the assumption that μ(Rn∖ARn)<∞, we show that X satisfies (H) if and only if the equation Ay=−a−∫{x∈Rn∖ARn:|x|<1}xμ(dx),y∈Rn, has at least one solution. Finally, we show that if X is a subordinator and satisfies (H) then its drift coefficient must be 0.

Keywords: Hunt’s hypothesis; Getoor’s conjecture; Lévy processes (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.03.013

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