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arXiv · 2112.12558

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

Jonas Arista·Elia Bisi·Neil O'Connell
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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.

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Jonas Arista, Elia Bisi, Neil O'Connell. 2022-09-23. Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices. https://doi.org/10.1214/22-aihp1338

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