Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices.

Abstract: We establish analogues of the geometric Pitman 2M−X theorem of Matsumoto and Yor and of the classical Dufresne identity, for a multiplicative random walk on positive definite matrices with Beta type II distributed increments. The Dufresne type identity provides another example of a stochastic matrix recursion that admits an explicit solution.