Matsumoto-Yor processes on Jordan algebras

• 成果类型: Article; Early Access
• 署名作者: Chhaibi, Reda; Defosseux, Manon
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01455-9
• 发表日期: 2025-11-28
• 关键词: Pitman's theorem; Brownian motion on Lie groups and symmetric spaces; Matsumoto-Yor property; Intertwining of semi-groups; jordan algebras; EXPONENTIAL WIENER FUNCTIONALS; pitmans 2m-x theorem; analog

摘要

The process (integral 0te2bs-btdst >= 0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\int _0<^>t e<^>{2b_s-b_t}\, ds\;\ t\ge 0)$$\end{document}, where b is a real Brownian motion, is known as the geometric 2M-X Matsumoto-Yor process. Remarkably, it enjoys the Markov property. We provide a generalization of this process in the context of Jordan algebras, and we prove the Markov property for this generalization.Our Markov process occurs as a limit of discrete-time AX+B Markov chains on the cone of squares whose invariant probability measures classically yield a Dufresne-type identity for a perpetuity. In particular, the paper provides a generalization to any symmetric cone of the matrix-valued generalization of the Matsumoto-Yor process and Dufresne identity initially developed by Rider-Valk & oacute;.