An analogue of Pitman's 2M-X theorem for exponential Wiener functionals - Part II: The role of the generalized inverse Gaussian laws

In Part I of this work, we have shown that the stochastic process Z((mu)) d efined by 8.1 below is a diffusion process, which may be considered as an e xtension of Pitman's 2M - X theorem. In this Part II, we deduce from an ide ntity in law partly due to Dufresne that Z((mu)) is intertwined with Browni an motion with drift mu and that the intertwining kernel may be expressed i n terms of Generalized Inverse Gaussian laws.