论文标题
Ornstein-uhlenbeck的界变化过程
Ornstein-Uhlenbeck processes of bounded variation
论文作者
论文摘要
引入了有界变异的Ornstein-Uhlenbeck过程，作为Langevin方程的类似物的解决方案，其综合电报过程取代了Brownian运动。有一个间隔$ i $，使得从$ i $的内部点开始的过程始终保留在$ i $之内。从外面开始，此过程a。 s。在有限的时间内达到此间隔。显式获得该过程落入此间隔的时间的分布。 该过程的平均值和方差的某些公式是根据电报过程的联合分布及其集成副本获得的。 在KAC的重新缩放下，极限过程被确定为经典的Ornstein-Uhlenbeck过程。
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting from the internal point of $I$ always remains within $I$. Starting outside, this process a. s. reaches this interval in a finite time. The distribution of the time for which the process falls into this interval is obtained explicitly. The certain formulae for the mean and the variance of this process are obtained on the basis of the joint distribution of the telegraph process and its integrated copy. Under Kac's rescaling, the limit process is identified as the classical Ornstein-Uhlenbeck process.
