Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917218191671296 |
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| author | Arista, Jonas Bisi, Elia O'Connell, Neil |
| author_facet | Arista, Jonas Bisi, Elia O'Connell, Neil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12558 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices Arista, Jonas Bisi, Elia O'Connell, Neil Probability Mathematical Physics 60K35, 82B23, 60B20 (Primary), 60G10, 22E30, 62H10 (Secondary) 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. |
| title | Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices |
| topic | Probability Mathematical Physics 60K35, 82B23, 60B20 (Primary), 60G10, 22E30, 62H10 (Secondary) |
| url | https://arxiv.org/abs/2112.12558 |