Which distributions have the Matsumoto-Yor property?

The Matsumoto–Yor property on trees

Viewing the Matsumoto–Yor property as a bivariate property with respect to the simple tree with two vertices and one edge, we extend it to a p-variate property with respect to any tree with p vertices. The converse of the Matsumoto–Yor property, which characterizes the product of a gamma and a generalized inverse Gaussian distribution, is extended to characterize the product of a gamma and p 1 ...

On Ideals Which Have the Weakly Insertion of Factors Property

A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...

Kummer and gamma laws through independences on trees - Another parallel with the Matsumoto-Yor property

on ideals which have the weakly insertion of factors property

a one-sided ideal of a ring has the insertion of factors property (or simply, ifp) if implies r for . we say a one-sided ideal of has the weakly ifp if for each , implies , for some non-negative integer . we give some examples of ideals which have the weakly ifp but have not the ifp. connections between ideals of which have the ifp and related ideals of some ring extensions are also shown.

Positivity preserving forms have the Fatou property

If (un)n∈IN is a sequence in L2(E; m) converging m-almost everywhere to u, then Fatou’s lemma says that (u, u)L2 ≤ lim infn(un, un)L2 , where we set (u, u)L2 = ∞ if u 6∈ L2(E; m). The corresponding result, where a Dirichlet form replaces the inner product, was used by Silverstein [5; Lemma 1.7] and by Fukushima, Oshima, and Takeda [2; Theorem 1.5.2] to define extended Dirichlet space and study ...