On the distribution of suprema of random processes from the space \(\text{Sub}_{\varphi}(\Omega)\). (Ukrainian. English summary) Zbl 0970.62033

We study separable stochastic processes which are defined on a compact set and belong to a space of random variables \(\text{Sub}_{\varphi}(\Omega)\). For such processes estimations of the distribution of its suprema in the case where the process and its increments belong to different spaces and conditions for sample path continuity with probability one of the process from \(\text{Sub}_{\varphi}(\Omega)\) are found.


62G32 Statistics of extreme values; tail inference
60G70 Extreme value theory; extremal stochastic processes
62G05 Nonparametric estimation
60G07 General theory of stochastic processes