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.

引入有界变化的Ornstein-Uhlenbeck过程作为Langevin方程类似物的解决方案，并使用集成电报过程代替了Brownian运动。有一个间隔I，从I的内部点开始的过程始终保持在I内。从外部开始，此过程在有限时间内达到此间隔。明确获得过程落入该时间间隔的时间分布。该过程的均值和方差的某些公式是在电报过程及其综合副本的联合分布的基础上获得的。在Kac的缩放后，极限过程被确定为经典的Ornstein-Uhlenbeck过程。