首页|An infinite-dimensional representation of the Ray-Knight theorems
An infinite-dimensional representation of the Ray-Knight theorems
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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 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(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.
Ray-Knight theoremμ-processwhite noiseTanaka's formula
Elie A?dékon、Yueyun Hu、Zhan Shi
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School of Mathematical Sciences,Fudan University,Shanghai 200433,China
LAGA,Université Sorbonne Paris Nord,Villetaneuse 93430,France
Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
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