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August, 1982 Structure of a Class of Operator-Selfdecomposable Probability Measures
Zbigniew J. Jurek
Ann. Probab. 10(3): 849-856 (August, 1982). DOI: 10.1214/aop/1176993796


In 1972, K. Urbanik introduced the notion of operator-selfdecomposable probability measures (originally they were called Levy's measures). These measures are identified as limit distributions of partial sums of independent Banach space-valued random vectors normed by linear bounded operators. Recently, S. J. Wolfe has characterized the operator-selfdecomposable measures among the infinitely divisible ones. In this note we find examples of measures whose finite convolutions are a dense subset in a class of all operator-selfdecomposable ones.


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Zbigniew J. Jurek. "Structure of a Class of Operator-Selfdecomposable Probability Measures." Ann. Probab. 10 (3) 849 - 856, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0489.60007
MathSciNet: MR659555
Digital Object Identifier: 10.1214/aop/1176993796

Primary: 60B10
Secondary: 60F05

Keywords: Banach space , generalized Poisson exponent , infinitely divisible measure , one-parameter semi-group of bounded linear operators , operator-selfdecomposable measures

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
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