Minimax prediction of random processes with stationary increments from observations with stationary noise

We deal with the problem of mean square optimal estimation of linear functionals which depend on the unknown values of a random process with stationary increments based on observations of the process with noise, where the noise process is a stationary process. Formulas for calculating values of the mean square errors and the spectral characteristics of the optimal linear estimates of the functionals are derived under the condition of spectral certainty, where the spectral densities of the processes are exactly known. In the case of spectral uncertainty, where the spectral densities of the processes are not exactly known while a class of admissible spectral densities is given, relations that determine the least favorable spectral densities and the minimax robust spectral characteristics are proposed.