On the distribution of the trajectory maximum of a random walk with switchings

摘要

We continue studying of the random walk introduced in [1].The distribution of the random walk jumps changes under successiveachievement regulatory boundaries. The regulation is intended to keepunder control the range of trajectories. At the same time the structureof the process allows the trajectories stay some time outside the bandadjustments. The paper establishes limit theorems for the distributionof the maximum possible excess of the upper regulatory barrier.