  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.
