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Laplace Transforms via Hadamard Factorization

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Laplace Transforms via Hadamard Factorization
2.	Creator	Author's name, affiliation, country	Fuchang Gao; University of Idaho
2.	Creator	Author's name, affiliation, country	Jan Hannig; Colorado State University
2.	Creator	Author's name, affiliation, country	Tzong-Yow Lee; University of Maryland
2.	Creator	Author's name, affiliation, country	Fred Torcaso; The Johns Hopkins University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Small ball probability, Laplace Transforms, Hadamard's factorization theorem.
3.	Subject	Subject classification	Primary 60G15
4.	Description	Abstract	In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared $L_2$ norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can be expressed in terms of well understood functions using complex-analytic theorems on infinite products, in particular, the Hadamard Factorization Theorem. Together with some tools from linear differential operators, we show that in many cases the Laplace transforms can be obtained with little work. We demonstrate this on several examples. Of course, once the Laplace transform is known explicitly one can easily calculate the corresponding exact $L_2$ small ball probabilities using Sytaja Tauberian theorem. Some generalizations are mentioned.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Research of F. Gao was partially supported by NSF grant EPS-0132626 and a seed grant from the University of Idaho
7.	Date	(YYYY-MM-DD)	2003-08-19
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/151
10.	Identifier	Digital Object Identifier	10.1214/EJP.v8-151
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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