Prediction problem for continuous time stochastic processes with periodically correlated increments observed with noise
Abstract
We propose solution of the problem of the mean square optimal estimation of linear functionalswhich depend on the unobserved values of a continuous time stochastic process with periodicallycorrelated increments based on observations of this process with periodically stationary noise. Tosolve the problem, we transform the processes to the sequences of stochastic functions which forman infinite dimensional vector stationary sequences. In the case of known spectral densities of thesesequences, we obtain formulas for calculating values of the mean square errors and the spectralcharacteristics of the optimal estimates of the functionals. Formulas determining the least favorablespectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates offunctionals are derived in the case where the sets of admissible spectral densities are given.References
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