论文标题
射线骑士定理的无限维度表示
An infinite-dimensional representation of the Ray-Knight theorems
论文作者
论文摘要
布朗运动的经典射线骑士定理决定了其本地时间过程的定律，要么是在当地时间在特定值a的第一次击打时间，要么在布朗尼运动的第一次达到给定位置b的时间。我们通过与适当的白噪声相对于随机积分共同描述所有A和所有B的局部时间过程，从而扩展了这些结果。我们的结果适用于$ $ $ - 过程，并有立即应用：$μ$ - 过程是偶然连续分支过程（CSBP）的高度过程（CSBP）（Lambert [10]），而feller csbp却带有移民的CSBP，可以满足由静止的差异方程式的驱动的（dandson vires tripection and Lie noise verned a Diredial direds and li noise verne and li noise verne and li noise dive and li noise and li noise and li噪声[7] dawawsson;我们的结果给出了这两个描述之间的明确关系，并表明所讨论的随机微分方程是对田中公式的重新制定。
The classical Ray-Knight theorems for Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin, or at the first hitting time of a given position b by Brownian motion. We extend these results by describing the local time process jointly for all a and all b, by means of stochastic integral with respect to an appropriate white noise. Our result applies to $μ$-processes, and has an immediate application: a $μ$-process is the height process of a Feller continuous-state branching process (CSBP) with immigration (Lambert [10]), whereas a Feller CSBP with immigration satisfies a stochastic differential equation driven by a white noise (Dawson and Li [7]); our result gives an explicit relation between these two descriptions and shows that the stochastic differential equation in question is a reformulation of Tanaka's formula.
