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

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  • Hu, Ze-Chun
  • Sun, Wei

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.

Suggested Citation

  • Hu, Ze-Chun & Sun, Wei, 2012. "Hunt’s hypothesis (H) and Getoor’s conjecture for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2319-2328.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2319-2328
    DOI: 10.1016/j.spa.2012.03.013
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