Publication: Asymptotic behaviour of the Urbanik semigroup
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Date
2015
Authors
Berg, Christian
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Publisher
Elsevier
Acceso abierto / Sarbide irekia
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Versión aceptada / Onetsi den bertsioa
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Abstract
We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c is indeterminate as Stieltjes moment sequence if and only if c > 2. When c is a natural number ec is a Meijer-G function. From the results about ec we obtain the asymptotic behaviour at 1 of the convolution roots of the Gumbel distribution.
Description
Keywords
Product convolution semigroup, Asymptotic approximation of integrals, Laplace and saddle point methods, Moment problems, Gumbel distribution
Department
Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza
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