Lamperti关系的多维版本与Matsumoto-Yor过程
概率论
2023-06-06 v1
摘要
本文给出了与漂移项布朗运动的指数泛函相关的Matsumoto-Yor性质的多维推广。该推广涉及由有限加权图顶点索引的几何布朗运动之间的相互作用，以及该图上顶点增强跳跃过程相关的随机势。在此背景下，我们证明了Lamperti变换、Matsumoto-Yor过程的马尔可夫性以及交织关系的对应结论。
引用
@article{arxiv.2306.02158,
title = {A multi-dimensional version of Lamperti's relation and the Matsumoto-Yor processes},
author = {Thomas Gérard and Valentin Rapenne and Christophe Sabot and Xiaolin Zeng},
journal= {arXiv preprint arXiv:2306.02158},
year = {2023}
}
备注
Extended version of arXiv:2004.10692 with a new author Keywords: exponential functional of Brownian motion, Inverse Gaussian law, vertex reinforced jump process, Pitman 2M-B theorem, Pitman transform