Record link: 
http://hdl.handle.net/20.500.12708/205452
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Title: 
Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices
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Citation: 
Arista, J., Bisi, E., & O’Connell, N. (2024). Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 60(2), 923–945. https://doi.org/10.1214/22-AIHP1338
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Publisher DOI: 
10.1214/22-AIHP1338
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Arista, Jonas 
Bisi, Elia 
O’Connell, Neil 
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Organisational Unit: 
E105-07 - Forschungsbereich Wahrscheinlichkeitstheorie 
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Journal: 
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 
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ISSN: 
0246-0203
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Date (published): 
1-May-2024
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Number of Pages: 
23
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Publisher: 
INST MATHEMATICAL STATISTICS-IMS
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Peer reviewed: 
Yes
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Keywords: 
Intertwining relations; Lyapunov exponents; Matrix Dufresne identity; Matrix Matsumoto-Yor theorem; Matrix variate distributions; Stochastic matrix recursions and equations; Wishart and Beta distributions
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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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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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