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 $\int_0^1ξ_tdt$, using the random variables $ξ_{τ_1},\dots, ξ_{τ_n}$ as an information set, where $τ_1,\dots, τ_n$ are random variables. We also consider the problem of the information set optimization.

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