Matsumoto--Yor processes on Jordan algebras
| Autor: | Chhaibi, Reda, Defosseux, Manon |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The process $(\int_0^t e^{2b_s-b_t}\, ds\ ;\ t\ge 0)$ where $b$ is a real Brownian motion is known as the geometric 2M-X Matsumoto--Yor process, and it enjoys a miraculous Markov property. We provide a generalization of this process to the context of Jordan algebras, and we prove the Markov property. Our Markov process occurs as a limit of a sequence of Markov chains on the cone of squares which involve AX+B Markov chains whose invariant probability measures classically provide a Dufresne--type identity for a perpetuity. In particular, the paper gives in a generalization to any symmetric cones of the initial matrix generalization of Matsumoto--Yor process and Dufresne identity by Rider--Valko. Comment: v1: 31 pages. Preliminary version. Comments are welcome |
| Databáze: | arXiv |
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