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How many Laplace transforms of probability measures are there?
Author(s):
Fuchang
Gao;
Wenbo
V.
Li;
Jon A.
Wellner
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4331-4344.
MSC (2010):
Primary 46B50, 60G15, 60G52;
Secondary 62G05
Posted:
May 24, 2010
MathSciNet review:
2680059
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Additional information
Abstract:
A bracketing metric entropy bound for the class of Laplace transforms of probability measures on  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:
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
Posted:
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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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