THE MARKOV PROPERTY OF LOCAL TIMES OF BROWNIAN MOTION INDEXED BY THE BROWNIAN TREE
成果类型：
Article
署名作者：
Le Gall, Jean-Francois
署名单位：
Universite Paris Saclay
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/23-AOP1652
发表日期：
2024
页码：
188-216
关键词：
摘要：
We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model the total occupation measure is known to have a continuously differentiable density (l(x))(x is an element of R), and we write (l(x))(x is an element of R )for its derivative. Although the process (l(x))(x >= 0) is not Markov, we prove that the pair(l(x), l(x))(x >= 0 )is a time-homogeneous Markov process. We also establish a similar result for the local times of one-dimensional super-Brownian motion. Our methods rely on the excursion theory for Brownian motion indexed by the Brownian tree.