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Article Dans Une Revue Bernoulli Année : 2012

Independence properties of the Matsumoto–Yor type

Résumé

We define Letac-Wesolowski-Matsumoto-Yor (LWMY) functions as decreasing functions from (0, ∞) onto (0, ∞) 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. We prove, under additional assumptions, that there are essentially four such functions. 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 generalized inverse Gaussian while Y is gamma-distributed. In the three other cases, the associated densities are provided. As a consequence, we obtain a new relation of convolution involving gamma distributions and Kummer distributions of type 2.
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Dates et versions

hal-01284025 , version 1 (07-03-2016)

Identifiants

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Angelo Efoévi Koudou, Pierre Vallois. Independence properties of the Matsumoto–Yor type. Bernoulli, 2012, 18 (1), pp.119-136. ⟨10.3150/10-BEJ325⟩. ⟨hal-01284025⟩
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