An analogue of Pitman’s 2M – X theorem for exponential Wiener functionals: Part I: A time-inversion approach

Abstract

Let be a one-dimensional Brownian motion with constant drift µ ∈ R starting from 0. In this paper we show thatgives rise to a diffusion process and we explain how this result may be considered as an extension of the celebrated Pitman’s 2M - X theorem. We also derive the infinitesimal generator and some properties of the diffusion process and, in particular, its relation to the generalized Bessel processes.