Robust extrapolation problem for random processes with stationary increments

Abstract

The problem of optimal estimation of linear functionals $A\hat{I}¾={\int }_0^{\infty }a(t)\hat{I}¾(t)dt$ and $A_T\hat{I}¾={\int }_0^{T}a(t)\hat{I}¾(t)dt$ depending on the unknown values of random process $\hat{I}¾(t)$, $t\in R$, with stationary $n$th increments from observations of ttis process for $t<0$ is considered. Formulas for calculating mean square error and spectral characteristic of optimal linear estimation of the functionals are proposed in the case when spectral density is exactly known. Formulas that determine the least favorable spectral densities are proposed for given sets of admissible spectral densities.