Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Multiplicative Cauchy functional equation in the cone of positive-definite symmetric matrices

100%

Bobecka K., Wesołowski J.

Annales Polonici Mathematici

2003

tom 82

nr 1

1-7

We solve the multiplicative Cauchy equation for real functions of symmetric positive definite matrices under the differentiability restriction. The specialty of the problem lies in the symmetry of the multiplication.

The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"

100%

Bobecka K., Wesołowski J.

Studia Mathematica

2002

tom 152

nr 2

147-160

The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason such an extension is possible, is the assumed property of invariance of the distribution of the "quotient" (properly defined for matrices). The main result of this paper is that the matrix variate Lukacs theorem holds without any invariance assumption for the "quotient". The argument is based on solutions of some functional equations in matrix variate real functions, which seem to be of independent interest. The proofs use techniques of differential calculus in the cone of positive definite symmetric matrices.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Bobecka K.

2 Wesołowski J.

1 2003

1 2002

Wyniki wyszukiwania

Multiplicative Cauchy functional equation in the cone of positive-definite symmetric matrices

The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"