论文标题
布朗（Brownian Tree）索引的布朗尼运动当地时代的马尔可夫属性
The Markov property of local times of Brownian motion indexed by the Brownian tree
论文作者
论文摘要
我们考虑了布朗（Brownian）树索引的布朗运动模型，该模型在概率，统计物理学和组合学方面出现在各种不同的情况下。对于此模型，已知总职业措施具有连续可区分的密度。尽管非负真实索引的密度过程不是马尔可夫，但我们证明由密度及其衍生物组成的对是一个时间均匀的马尔可夫过程。我们还为一维超棕色运动的当地时代建立了类似的结果。我们的方法依赖于布朗树索引的布朗运动的旅行理论。
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. Although the density process indexed by nonnegative reals is not Markov, we prove that the pair consisting of the density and its derivative 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.
