Asymptotic behaviour of the Urbanik semigroup
Fecha
2015Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1016/j.jat.2014.05.006
Resumen
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
...
[++]
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. [--]
Materias
Product convolution semigroup,
Asymptotic approximation of integrals,
Laplace and saddle point methods,
Moment problems,
Gumbel distribution
Editor
Elsevier
Publicado en
Journal of Approximation Theory 195 (2015) 109-121
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
The first author has been supported by grant 10-083122 from The Danish Council for Independent Research/Natural Sciences. The second author has been supported by grant MTM2010-21037 from the Dirección General de Ciencia y Tecnología.