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].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Infinite Dimensional Analysis, Quantum Probability and Related Topics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.