The problem of optimal linear estimation of the functional ___ that depends on the unknown values of a harmonizable α−stable stochastic processes ____ from observations of the process ___at points ___, where ___ and ___ are mutually independent harmonizable α−stable processes, is considered. Formulas for calculating the error and the spectral characteristic of the optimal estimate of the functional ___ are proposed in the case of spectral certainty where spectral densities of the processes are exactly known. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed in the case of spectral uncertainty for some classes of admissible spectral densities.

Cambanis, S. Complex stable variables and processes // Contributions to Statistics: Essays in Honor of Norman L. Johnson, P. K. Sen, ed., NorthHolland, New York - 1983. - P. 63-79.

Cambanis, S., Masry, E. Spectral density estimation for stationary stable processes // Stoch. Process. Applications. - 1984. - 18, N.1. - P. 1-31.

Cambanis, S., Soltani, R. Prediction of stable processes: Spectral and moving average representations// Z. Wahrsch. Verw. Gebiete. - 1984. - 66, - P. 593-612.

Grenander, U. A prediction problem in game theory // Ark. Mat. - 1957. - 3, - P. 371-379.

Hosoya, Y. Harmonizable stable processes.// Z. Wahrsch. Verw. Gebiete. - 1982. - 60, - P. 517-533.

Kassam S. A., Poor H. V. Robust techniques for signal processing: A survey// Proceedings of the IEEE. - 1985. - 73, N.3. - P. 433-481.

Kolmogorov A. N Collection of articles. Volume. II: Probability theory and mathematical statistics. Ed. AND. N. Shiryaev. Mathematics and its applications. — M.: Nauka, 1986. — 535 c.

Luz M., Moklyachuk M. Robust extrapolation problem for stochastic processes with stationary increments// Mathematics and Statistics. – 2014. – 1, N.2. - P. 78-88.

Luz M., Moklyachuk M. Minimax interpolation problem for random processes with stationary increments// Statistics, Optimization & Information Computing. - 2015. -3, - P. 30-41.

Luz M., Moklyachuk M. Filtering problem for random processes with stationary increments// Contemporary Mathematics and Statistics. – 2015. – 3, N.1. - P. 8-27.

Moklyachuk M. P. Robust procedures in time series analysis// Theory of Stochastic Processes. - 2000. - 6, N.3-4. - P. 127-147.

Moklyachuk M. P. Game theory and convex optimization methods in robust estimation problems// Theory of Stochastic Processes. - 2001. - 7, N.1-2. - P. 253-264.

Moklyachuk M. P. Robust estimates of functionals from stochastic processes. — K.: VPC "Kyiv University 2008. — 320 p.

Moklyachuk M. P. Minimax-robust estimation problems for stationary stochastic sequences//Statistics, Optimization & Information Computing. – 2015. – 3, N.4. – P. 348-419.

Moklyachuk M., Golichenko I. Periodically correlated processes estimates. — LAP Lambert Academic Publishing, 2016. — 308 p.

Moklyachuk M., Masyutka O. Minimaxrobust estimation technique for stationary stochastic processes.—LAPLambertAcademicPublishing, 2012. — 296 p.

Moklyachuk M. P., Ostapenko V. I. Minimax interpolation problem for harmonizable stable sequences with noise observations// J. Appl. Math. Stat. – 2015. – 2, N.1. – P. 21-42.

Moklyachuk M. P., Ostapenko V. I. Minimax interpolation of harmonizable sequences// Theor. Probability and Math. Statistics. - 2016. - N.92. – P. 135–146.

Pourahmadi, M. On minimality and interpolation of harmonizable stable processes. // SIAM J. Appl. Math. - 1984. - 44, N.5. – P. 1023-1030.

Rajput, S., Sundberg, C. On some extremal problems in Hp and the prediction of Lp - harmonizable stochastic processes // Probability Theory and Related Fields. - 1994. - 99, N.2. - P. 197-210.

Rockafellar, R. T. Convex Analysis. — Princeton: University Press, 1997. — 451 p.

Pshenichny B.N. Necessary conditions of extremum. — M.: Nauka, 1982. — 144 p.

Singer, I. Best Approximation in Normed LinearSpacesbyElementsofLinearSubspaces.—BerlinHeidelberg-New York: Springer-Verlag, 1980—415 p.

Vastola, K. S., Poor, H. V. An analysis of the effects of spectral uncertainty on Wiener filtering // Automatica. - 1983. - 28, - P. 289-293.

Weron, A. Harmonizable stable processes on groups: spectral, ergodic and interpolation properties. // Z. Wahrsch. Verw. Gebiete - 1985. - 68, N.4. - P. 473-491.

Wiener, N. Extrapolation, interpolation and smoothing of stationary time series. With engineering applications. — The M. I. T. Press, Massachusetts Institute of Technology, Cambridge, Mass., 1966. — 163 p.

Yaglom A.M. Extrapolation, interpolation and filtering of stationary random processes with rational spectral density // Proceedings of the Moscow Mathematical Society – 1955. – N.4 – P. 333-374.

Yaglom A. M. Correlation theory of stationary and related random functions. Vol. 1: Basic results. — Springer Series in Statistics, Springer-Verlag, New York etc., 1987. — 526 p.

Yaglom A. M. Correlation theory of stationary and related random functions. Vol. 2: Supplementary notes and references. — Springer Series in Statistics, Springer-Verlag, New York, etc., 1987. — 258 p.