The Time Inversion Method
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.
KeywordsBrownian Motion Local Time Time Inversion Borel Function Bessel Process
Unable to display preview. Download preview PDF.