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

Abstract

Let be a one-dimensional Brownian motion with constant driftµ∈ R starting from 0. In this paper we show that gives rise to a diffusion process and we explain how this result may be considered as an extension of the celebrated Pitman’s2M - Xtheorem. We also derive the infinitesimal generator and some properties of the diffusion process and, in particular, its relation to the generalized Bessel processes.

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