论文标题
部分可观测时空混沌系统的无模型预测
Inverting Ray-Knight identities on trees
论文作者
论文摘要
在本文中，我们首先介绍了与树木上的强度$α（\ ge 0）$相关的射线骑士身份和渗透射线骑士身份。然后，我们介绍上述身份的反转，这些倒数是用排斥跳跃过程来表达的。特别是，在$α= 0 $的情况下，倒置给出了马尔可夫跳跃过程的有条件定律，鉴于其本地时间字段。我们进一步表明，这些排斥跳跃过程的细网限是自我re缩扩散\ cite {aidekon}，参与相应的度量图上的射线骑士身份的反转。这是\ cite {2016 inverting，lupu2019inverting，lupuejp657}中的结果的概括，在其中，作者探索了一般图上$α= 1/2 $的情况。我们的构造与\ cite {2016 inverting，lupu2019inverting}，并基于随机网络和环汤之间的联系。
In this paper, we first introduce the Ray-Knight identity and percolation Ray-Knight identity related to loop soup with intensity $α(\ge 0)$ on trees. Then we present the inversions of the above identities, which are expressed in terms of repelling jump processes. In particular, the inversion in the case of $α=0$ gives the conditional law of a Markov jump process given its local time field. We further show that the fine mesh limits of these repelling jump processes are the self-repelling diffusions \cite{Aidekon} involved in the inversion of the Ray-Knight identity on the corresponding metric graph. This is a generalization of results in \cite{2016Inverting,lupu2019inverting,LupuEJP657}, where the authors explore the case of $α=1/2$ on a general graph. Our construction is different from \cite{2016Inverting,lupu2019inverting} and based on the link between random networks and loop soups.
