仿射凹室区间上的Pitman变换和布朗运动
Pitman transforms and Brownian motion in the interval viewed as an affine alcove
摘要：
Pitman定理指出，如果{Bt，t $\ge$ 0}是一维布朗运动，则{Bt - 2 inf s $\le$ t Bs，t $\ge$ 0}是三维贝塞尔过程，即在Doob意义下条件为永远保持正的布朗运动。本文给出了区间上布朗运动的一个类似表示。由于双势垒的存在，它更加复杂，而且只是渐近的。这利用了区间是仿射李代数A 1 1的凹室的事实。
英文摘要：
Pitman's theorem states that if {Bt, t $\ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$\le$t Bs, t $\ge$ 0} is a three dimensional Bessel process, i.e. a Brownian motion conditioned in Doob sense to remain forever positive. In this paper one gives a similar representation for the Brownian motion in an interval. Due to the double barrier, it is much more involved and only asymptotic. This uses the fact that the interval is an alcove of the Affine Lie algebra A 1 1 .
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