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

N. V. Prokhorenko (Kruglova)
Theory of Stochastic Processes
Vol.21 (37), no.1, 2016, pp.73-83
In this paper we compute the probability $\Pb\left\{\sup_{t\in [T_1,T_2]}(w(t)-h(t))<0\right\},$ 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.