On some generalizations of the results about the distribution of the maximum of the Chentsov random field on polygonal lines

In this paper we compute the probability $\mathbf{P}\left\{\sup_{t\in [T_1,T_2]}(w(t)-h(t))<0\right\},$ where $w(t)$ is a Wiener process and $h$ is a step-wise linear function. We use it to obtain the distribution of the maximum of the Chentsov random field on polygonal lines. We have considerably expanded a class of such polygonal lines in this paper.