HOW MANY LAPLACE TRANSFORMS OF PROBABILITY MEASURES ARE THERE?

A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) 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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Veröffentlicht in:	Proceedings of the American Mathematical Society 2010-12, Vol.138 (12), p.4331-4344
Hauptverfasser:	GAO, FUCHANG, LI, WENBO V., WELLNER, JON A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Banach space Entropy Exact sciences and technology General mathematics General, history and biography Integers Laplace transformation Mathematical functions Mathematics Maximum likelihood estimation Monotonic functions Probabilities Probability and statistics Probability theory and stochastic processes Probability theory on algebraic and topological structures Sciences and techniques of general use Statistics Stochastic processes
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Zusammenfassung:	A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) 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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-2010-10448-3