Independence properties of the Matsumoto-Yor type (Q408091)

The object of this paper are Letac-Wesolowski-Matsumoto-Yor (LWMY) functions. These are decreasing functions from \((0,\infty)\) onto \((0,\infty)\) 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 authors prove that under additional assumptions there are essentially four such functions.