On the remarkable Lamperti representation of the inverse local time of a radial Ornstein-Uhlenbeck process

Abstract

We give a description, in terms of ``pseudo-stable increasing process'', of the Lamperti process associated with the inverse local time of a radial Ornstein-Uhlenbeck process. Following Bertoin-Yor, we also express, in two particular cases, the law of the perpetuity associated with this inverse local time.