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The range of a perturbed Lévy process
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  • Published: May 1989

The range of a perturbed Lévy process

  • S. N. Evans1 

Probability Theory and Related Fields volume 81, pages 555–557 (1989)Cite this article

Summary

A necessary and sufficient Fourier analytic condition is given for a real-valued Lévy process X to be such that all perturbations, X+f, of X by measurable functions f have range with positive Lebesgue measure. The condition is compared to one due to Kesten for the range of X alone to have positive Lebesgue measure, and in some cases it is found to coincide, whereas in others it is stronger.

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References

  1. Bretagnolle, J.: Résultats de Kesten sur les processus à accroissements indépendants. In: Séminaire de probabilités V, Strasbourg 1971. (Lect. Notes Math., vol. 191) Berlin Heidelberg New York: Springer 1971

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  2. Kahane, J-P.: Some random series of functions. Lexington: Heath 1968

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  3. Kesten, H.: Hitting probabilities of single points for processes with stationary independent increments. Mem. Am. Math. Soc. vol.93. Providence: AMS 1969

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  4. Mountford, T.: Time inhomogeneous Markov processes and the polarity of single points. Ann. Probab., in press

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Mathematics-Astronomy Building, 22903, Chalottesville, VA, USA

    S. N. Evans

Authors
  1. S. N. Evans
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Additional information

Partially supported by NSF grant DMS 8701212

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Cite this article

Evans, S.N. The range of a perturbed Lévy process. Probab. Th. Rel. Fields 81, 555–557 (1989). https://doi.org/10.1007/BF00367302

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  • Received: 26 May 1988

  • Issue Date: May 1989

  • DOI: https://doi.org/10.1007/BF00367302

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Keywords

  • Fourier
  • Stochastic Process
  • Probability Theory
  • Measurable Function
  • Statistical Theory
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