Produit Beta-Gamma et régularité du signe

2012/07/27 by Thomas Simon, Simon, Thomas
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #math.CA #math.PR

paper · pdf · doi:10.48550/arxiv.1207.6464

arxiv created 2012/07/27 · arxiv updated 2012/07/30

Abstract

We study the total positivity of the multiplicative convolution kernel T associated with the independent product of two random variables B(a,b) and Γ(c). This kernel is totally positive of infinite order if b or d = a+b -c are integers. Otherwise the sign-regularity of T has always a finite order, which is here computed. More precisely, for every n≥ 1 it is shown that T is totally positive of order n + 1 if and only if (d,b) lies above a certain stairway \mathcal E_n plotted in the upper half-plane. This stairway also characterizes the sign-invariance of several determinants associated with the confluent hypergeometric function of the second kind.

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