On optimal recovery of integrals of random processes

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 ${\int }_0^1{\xi }_{t}dt$, 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.