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)


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)


Brownian Motion Local Time Sample Path Continuous Version Positive Lebesgue Measure 
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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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