Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Some changes of probabilities related to a geometric Brownian motion version of Pitman's 2M - X theorem.


Code(s) de Classification MSC:

Résumé: Rogers-Pitman have shown that the sum of the absolute value of $B^{\mu}$, Brownian motion with constant drift $\mu$, and its local time $L^{\mu}$ is a diffusion $R^{\mu}$. We exploit the intertwining relation between $B^{\mu}$ and $R^{\mu}$ to show that the same addition operation performed on a one-parameter family of diffusions $\{X^{(\alpha, \mu)}\}_{\alpha \in {\mathbb R}_+}$ yields the same diffusion $R^{\mu}$. Recently we obtained an exponential analogue of the Rogers-Pitman result. Here we exploit again the corresponding intertwining relationship to yield a one-parameter family extension of our result.

Mots Clés: Diffusion processes; Geometric Brownian motion; Markov intertwining kernel; (strict) local martingale; Explosion;

Date: 1999-04-25

Prépublication numéro: PMA-498