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Existence and Properties of Pseudo-Inverses for Bessel and Related Processes

Author

Listed:
  • Christophe Profeta

    (Université Nancy I)

  • Bernard Roynette

    (Université Nancy I)

  • Marc Yor

    (Université Paris VI)

Abstract

In Chapter 6, we have shown the existence of a decreasing pseudo-inverse for the martingale $(M_{t}:=\exp\left(B_{t}-\frac{t}{2}\right),t\geq0)$ . We shall now explore this notion in a more general framework, starting with the case of Bessel (and some related) processes. We show in particular that the tail probabilities of a Bessel process of index ν≥1/2 increase with respect to time; in fact it is the distribution function of a random time which is related to first and last passage times of Bessel processes.

Suggested Citation

Handle: RePEc:spr:sprfcp:978-3-642-10395-7_7
DOI: 10.1007/978-3-642-10395-7_7
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