Characterization of a class of infinitely divisible distributions in Hilbert space

1974 ◽  
Vol 16 (5) ◽  
pp. 1057-1060 ◽  
Author(s):  
V. M. Kruglov
Keyword(s):  
Hilbert Space ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

AN APPLICATION OF THE SEGAL–BARGMANN TRANSFORM TO THE CHARACTERIZATION OF LÉVY WHITE NOISE MEASURES

2010 ◽  
Vol 13 (02) ◽  
pp. 191-221 ◽  
Author(s):  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
White Noise ◽  
Probability Measures ◽  
Infinitely Divisible Distributions ◽  
Infinite Dimensions ◽  
Infinitely Divisible ◽  
Tempered Distributions ◽  
Bargmann Transform ◽  
Second Moment ◽  
Lévy White Noise

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].

scholarly journals Characterization of Hilbert space manifolds revisited

1986 ◽  
Vol 24 (1-3) ◽  
pp. 53-69 ◽  
Author(s):  
Mladen Bestvina ◽  
Philip Bowers ◽  
Jerzy Mogilsky ◽  
John Walsh
Keyword(s):  
Hilbert Space
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