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

N. V. Prokhorenko (Kruglova)

National Technical University of Ukraine ”KPI”, Department of Higher Mathematics No 1, Pr. Peremohy 37, 02056 Kiev, Ukraine

Abstract: 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.

Keywords: Wiener process; Chentsov random field; distribution of the supremum.

MSC: Primary 60G15; Secondary 60G60

Language: English

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