О распределении максимума траектории случайного процесса с переключениями

We study a stochastic process with switchings between two stationary processes with independent increments while achieving regulatory barriers. The regulation is intended to keep under control the range of trajectories. At the same time the structure of the process allows the trajectories stay some time outside the band adjustments. The paper establishes limit theorem for the distribution of the maximum possible excess of the upper regulatory barrier.