Kruglova N. On the distribution of some functionals of the Chentsov random field

In this thesis exact distribution of the maximum of the Chentsov field on polygonal lines with several points of break is investigated. Doob's transformations on the case of the Gaussian fields are generalized. The probabilities connected with the restriction of the d - dimensional Chentsov field on a surface are considered. Distribution of the maximum of the restriction of the Chentsov field on curves is investigated. Estimations of the tail of distribution of the maximum of the Chentsov field on polygonal line with one point of break are found. It is investigated asymptotic behaviour of distribution of the maximum of the Chentsov field on polygonal lines. It is proved, that asymptotic behaviour depends on the location of points of break.