Asymptotic behaviour of the Urbanik semigroup
classification
🧮 math.CV
math.PR
keywords
asymptoticbehavioursemigroupconvolutiondensitiesdeterminehalf-lineindeterminate
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We revisit the product convolution semigroup of probability densities e_c(t),c>0 on the positive half-line with moments (n!)^c and determine the asymptotic behaviour of e_c(t) for large and small t>0. This shows that (n!)^c is indeterminate as Stieltjes moment sequence if and only if c>2
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