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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

How many Laplace transforms of probability measures are there?


Authors: Fuchang Gao, Wenbo V. Li and Jon A. Wellner
Journal: Proc. Amer. Math. Soc. 138 (2010), 4331-4344
MSC (2010): Primary 46B50, 60G15, 60G52; Secondary 62G05
Published electronically: May 24, 2010
MathSciNet review: 2680059
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Abstract: A bracketing metric entropy bound for the class of Laplace transforms of probability measures on $ [0,\infty)$ is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.


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Additional Information

Fuchang Gao
Affiliation: Department of Mathematics, University of Idaho, Moscow, Idaho 83844
Email: fuchang@uidaho.edu

Wenbo V. Li
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: wli@math.udel.edu

Jon A. Wellner
Affiliation: Department of Statistics, University of Washington, Seattle, Washington 98195
Email: jaw@stat.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10448-3
PII: S 0002-9939(2010)10448-3
Keywords: Laplace transform, bracketing metric entropy, completely monotone functions, smooth Gaussian process, small deviation probability
Received by editor(s): September 15, 2009
Received by editor(s) in revised form: February 2, 2010
Published electronically: May 24, 2010
Additional Notes: The second author was supported in part by NSF grant DMS-0805929
The third author was supported in part by NSF Grant DMS-0804587 and NIH/NIAID Grant 5 R37 A1029168
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.