Efoevi Koudou, Université de Lorraine Homepage Independence properties of the Matsumoto-Yor type.
Abstract: We prove that, under smoothness assumptions, there are essentially four decreasing functions f defined on the positive real line with the following property : there exist independent, positive random variables X and Y such that the variables f(X+Y) and f(X)-f(X+Y) are independent. The first one is f(x)=1/x. In this case, referred to in the literature as the Matsumoto-Yor property, the law of X is the generalized inverse Gaussian distribution while Y is gamma distributed. We provide the associated densities in the three other cases, among which the Kummer distribution. We also write such an independence property in the case where X and Y are random matrices, where X follows a matrix Kummer distribution and Y a Wishart distribution. The main part of the talk is based on a joint work with Pierre Vallois. |