An Analogue of Pitman’s 2M — X Theorem for Exponential Wiener Functionals Part II: The Role of the Generalized Inverse Gaussian Laws

Abstract

In Part I of this work, we have shown that the stochastic process Z(µ) defined by (8.1) below is a diffusion process, which may be considered as an extension of Pitman’s 2M — X theorem. In this Part II, we deduce from an identity in law partly due to Dufresne that Z(µ) is intertwined with Brownian motion with drift µ and that the intertwining kernel may be expressed in terms of Generalized Inverse Gaussian laws.

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