SOME TRANSFORMATIONS OF DIFFUSIONS BY TIME REVERSAL
SOME TRANSFORMATIONS OF DIFFUSIONS BY TIME REVERSAL
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时间反转引起的扩散的一些转变
DOI：
10.1214/aop/1176994576
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发表时间：
1980
影响因子：
2.3
通讯作者：
M. Sharpe
中科院分区：
文献类型：
--
作者：
M. Sharpe
通过显式计算发现，一个贝塞尔扩散的状态最后退出时间和间隔占用时间的分布与其他贝塞尔扩散的首次通过时间分布是相同的。本文的目的是证明这些现象对于一类非常一般的线性扩散是持续存在的。这些证明不需要显式的计算，只依赖于用时间变化和反转的方法对马尔可夫过程进行变换的一些定理。最后，基于Revuz的测度，给出了主要工具——nagasawa时间反转定理的一个新的证明。基本过程将是一个正则扩散X，在区间（0,oo）上具有寿命D，满足假设
it was found by explicit calculations that the distributions of the last exit time from a state and occupation time of an interval for one Bessel diffusion are identical with first passage time distributions for certain other Bessel diffusions. The object of this paper is to show that these phenomena persist for a very general class of linear diffusions. The proofs are free of explicit calculations and depend only on some theorems on transformations of Markov processes by means of time change and reversal. At the end of the paper a new proof, based on the measures of Revuz, is given for the principal tool-Nagasawa's theorem on time reversal. The basic process will be a regular diffusion X with lifetime D on the interval (0, oo), satisfying the hypotheses