The Fourier-mehler Transform and Generalized Dilations of Gaussian and Poisson Measures


We deene a family of random dilations of the Wiener and Poisson measures, and show that they can be represented as generalised Fourier-Mehler transforms. These (not quasi invariant) transformations include transforms given e.g. by time changes on Brownian motion. The generators of one-parameter families of such transformations are computed, and the Poisson… (More)