论文标题
马尔可夫流程的当地时间结构由征收树索引
The structure of the local time of Markov processes indexed by Levy trees
论文作者
论文摘要
我们构建了当地时间的类似物 - 在固定点$ x $的情况下，我们为Levy Trees索引的Markov过程构建了类似物。首先，我们证明了Markov的征收树木索引的过程满足了Markov的特殊属性，可以将其视为古典Markov属性的空间版本。然后，我们通过近似程序构建当地时间的类似物，并表征其Lebesgue-Stieltjes度量的支持。我们还根据特殊的当地时代家庭提供了同等的结构。最后，结合了这些结果，我们表明Markov进程采用值$ x $编码新的征费树的点，并明确构建其高度过程。特别是，我们恢复了le gall的最新结果，该结果是关于布朗树的下属树，在该树中，下属函数是由布朗尼树索引的过去的最大布朗运动的最大过程给出的。
We construct the analogue of the local time -- at a fixed point $x$ -- for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees satisfy a special Markov property which can be thought as a spatial version of the classical Markov property. Then, we construct the analogue of the local time by an approximation procedure and we characterize the support of its Lebesgue-Stieltjes measure. We also give an equivalent construction in terms of a special family of exit local times. Finally, combining these results, we show that the points at which the Markov process takes the value $x$ encode a new Levy tree and we construct explicitly its height process. In particular, we recover a recent result of Le Gall concerning the subordinate tree of the Brownian tree where the subordination function is given by the past maximum process of Brownian motion indexed by the Brownian tree.
