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Efoevi Koudou, Université de Lorraine Print
Friday, 03 May 2013, 14:30 - 15:30

Efoevi Koudou, Université de Lorraine

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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 propertythe law of 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.

Location: Plaine
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