Minimax Interpolation Problem for Random Processes with Stationary Increments

The problem of mean-square optimal estimation of the linear functional AT ξ = ∫ T 0 a(t)ξ(t)dt that depends on the unknown values of a continuous time random process ξ(t), t ∈ R, with stationary nth increments from observations of the process ξ(t) at time points t ∈ R \ [0;T ] is investigated under the condition of spectral certainty as well as under the condition of spectral uncertainty. Formulas for calculation the value of the mean-square error and spectral characteristic of the optimal linear estimate of the functional are derived under the condition of spectral certainty where spectral density of the process is exactly known. In the case of spectral uncertainty where spectral density of the process is not exactly known, but a class of admissible spectral densities is given, relations that determine the least favourable spectral density and the minimax spectral characteristic are specified.