On the path of an inert object impinged on one side by a Brownian particle
On the path of an inert object impinged on one side by a Brownian particle
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在惰性物体一侧被布朗粒子撞击的路径上
DOI：
10.1007/s004400100160
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发表时间：
2001
影响因子：
2
通讯作者：
F. Knight
中科院分区：
文献类型：
--
作者：
F. Knight
抽象的。在R上的布朗粒子以t=0的速度撞击一个可以自由移动但不能通过的惯性质量。我们假设对于所有的t≥0，时间t的总动量传递是两个物体通过时间t接触的局部时间的常数K。证明了对于惯性质量的每个K>；0和初始速度V(0)，在布朗运动的自然过滤概率空间上，存在一个唯一的(定律中的)过程来描述这样的质量的路径。如果V(T)表示其速度，则当V(0)=0时，显式地得到了V(-1)(T)的定律，并讨论了它的性质。
Abstract. A Brownian particle on R impinges at t = 0 on an inertial mass which is free to move but cannot be passed. We assume that for all t≥ 0 the total transfer of momentum by time t is a constant K times the local time that the two objects are in contact by time t. It is proved that, for each K > 0 and initial velocity V(0) of the inertial mass, there is, on the natural filtered probability space of a Brownian motion, a unique (in law) process describing the path of such a mass. If V(t) denotes its velocity, the law of V(-1)(t) is obtained explicitly for V(0) = 0, and its properties are examined.