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"This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of population dynamics under the influence of environmental noise, reviews of methods of modeling of stochastic processes according to its probabilistic and statistical properties in various spaces of random variables with given reliability and accuracy, solution of the problem of mean square optimal estimation of unobserved values of periodically correlated stochastic sequences, and investigation of stability of time-inhomogeneous Markov chains"--
Stochastic processes. --- Stochastic processes --- Mathematical models.
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The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.
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