An infinite-dimensional representation of the Ray-Knight theorems  

作　　者：Elie Aidékon Yueyun Hu Zhan Shi 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China [2]LAGA,UniversitéSorbonne Paris Nord,Villetaneuse 93430,France [3]Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2024年第1期149-162,共14页中国科学（数学）（英文版）

基　　金：supported by ANR MALIN。

摘　　要：The classical Ray-Knight theorems for the 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 the Brownian motion.We extend these results by describing the local time process jointly for all a and b,by means of the stochastic integral with respect to an appropriate white noise.Our result applies toμ-processes,and has an immediate application:aμ-process is the height process of a Feller continuous-state branching process(CSBP)with immigration(Lambert(2002)),whereas a Feller CSBP with immigration satisfies a stochastic differential equation(SDE)driven by a white noise(Dawson and Li(2012));our result gives an explicit relation between these two descriptions and shows that the SDE in question is a reformulation of Tanaka’s formula.

关 键 词：Ray-Knight theorem μ-process white noise Tanaka's formula 

分 类 号：O175[理学—数学]