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The Time Inversion Method

  • Francis Hirsch
  • Christophe Profeta
  • Bernard Roynette
  • Marc Yor
Part of the B&SS — Bocconi & Springer Series book series (BS)

Abstract

Denote by (Λt, t ≥ 0) an integrable Lévy process, i.e. for any t ≥ 0, [¦Λt¦] < ∞. Then, (t Λ(1/t), t > 0) is a martingale in its natural filtration. Martingales of this type appear as being naturally associated to F1-type peacocks or peacocks defined from squared Bessel processes of dimension 0, or, more generally stable CSBP with index γ ] 1, 2]. We then generalize the preceding results of this chapter in Theorem 4.5, through a more abstract approach. Finally, we give examples of applications of that theorem.

Keywords

Brownian Motion Local Time Time Inversion Borel Function Bessel Process 
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

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Francis Hirsch
    • 1
  • Christophe Profeta
    • 2
  • Bernard Roynette
    • 2
  • Marc Yor
    • 3
    • 4
  1. 1.Laboratoire d’Analyse et ProbabilitésUniversité d’Évry-Val d’EssonneFrance
  2. 2.Institut Élie CartanUniversité Henri PoincaréNancy
  3. 3.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParis
  4. 4.Institut Universitaire de FranceFrance

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