AN APPLICATION OF THE SEGAL-BARGMANN TRANSFORM TO THE CHARACTERIZATION OF LEVY WHITE NOISE MEASURES

Being inspired by the observation that the Stein's identity is closely connected to the quantum decomposition of probability measures and the Segal-Bargmann transform, we are able to characterize the Levy white noise measures on the space S' of tempered distributions associated with a Levy spectrum having finite second moment. The results not only extends the Stein and Chen's lemma for Gaussian and Poisson distributions to infinite dimensions but also to many other infinitely divisible distributions such as Gamma and Pascal distributions and corresponding Levy white noise measures on S'.