Abstract
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 Lévy white noise measures on the space [Formula: see text] of tempered distributions associated with a Lévy 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 Lévy white noise measures on [Formula: see text].
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