On optimal recovery of integrals of random processes

Abstract

In this paper we prove a sharp Ostrowski type inequality for random processes of certain classes. This inequality is later applied to a solution of the optimal recovery of the integral $\int_0^1\xi_tdt$, using the random variables $\xi_{\tau_1},\dots, \xi_{\tau_n}$ as an information set, where $\tau_1,\dots, \tau_n$ are random variables. We also consider the problem of the information set optimization.