The Sde Solved by Local times of a Brownian Excursion or Bridge Derived from the Height Proole of a Random Tree or Forest
نویسنده
چکیده
Let B be a standard one-dimensional Brownian motion started at 0. Let Lt;v (jBj) be the occupation density of jBj at level v up to time t. The distribution of the process of local times (Lt;v(jBj);v 0) conditionally given Bt = 0 and Lt;0(jBj) = ` is shown to be that of the unique strong solution X of the It^ o SDE
منابع مشابه
The Sde Solved by Local times of a Brownian Excursion or Bridge Derived from the Height Profile of a Random Tree or Forest1 by Jim Pitman
Ž .. Ž . v 4 on the interval 0, V X , where V X inf v: H X du t , and X 0 t t 0 u v Ž . for all v V X . This conditioned form of the Ray Knight description of t Brownian local times arises from study of the asymptotic distribution as ' n and 2k n l of the height profile of a uniform rooted random forest of k trees labeled by a set of n elements, as obtained by conditioning a uniform random mapp...
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تاریخ انتشار 1997