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, as considered by Chamayou and Letac (J. Theoret. Probab. 12, 1999), that admits an explicit solution.

31 pages

References in corpus (3)

• Matrix Kesten Recursion, Inverse-Wishart Ensemble and Fermions in a Morse Potential
• Interacting diffusions on positive definite matrices
• Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity

Cited by in corpus (2)

• Matrix Whittaker processes
• Matsumoto-Yor processes on Jordan algebras