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The Behaviour and Construction of Local Times for Lévy Processes

  • Martin T. Barlow
  • Edwin A. Perkins
  • S. James Taylor
Part of the Progress in Probability and Statistics book series (PRPR, volume 9)

Abstract

The local time of a Lévy process Xt at a point a, denoted l t a (X), is a continuous increasing additive functional, which increases only on {t: Xt = a} If X is such that l t 0 exists, then as the transition probabilities of X are stationary in space, l t x will exist for every x ∈ ℝ, and we may therefore ask about the properties of the map (X,t,ω) → l t t (ω)

Keywords

Brownian Motion Local Time Sample Path Continuous Version Positive Lebesgue Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Martin T. Barlow
    • 1
  • Edwin A. Perkins
    • 3
  • S. James Taylor
    • 2
  1. 1.Statistical LaboratoryCambridgeUK
  2. 2.Dept. of MathematicsUniversity of VirginiaCharlottesvilleUSA
  3. 3.Dept. of MathematicsUniversity of British ColumbiaVancouverCanada

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