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The quantization in time of sample functions of differentiable Gaussian processes
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1991), pp. 17-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper algorithms of approximation of two classes of Gaussian stationary processes are suggested, when it is supposed that the sample functions are differentiable one time or two. In both cases asymptotic formulas for the approximating regression processes and for the variances of the processes of deviations are obtained. These results make possible to get recommendations on choosing the optimal step of quantization. 
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A. H. Simonian; V. R. Fatalov. The quantization in time of sample functions of differentiable Gaussian processes. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1991), pp. 17-24. http://geodesic.mathdoc.fr/item/UZERU_1991_1_a2/

[1] Yu. K. Belyaev, A. Kh. Simonyan, V. A. Krasavkina, “Kvantovanie po vremeni realizatsii nedifferentsiruemykh gaussovskikh protsessov”, Izv. AN SSSR. Ser. tekhn. kibern., 1976, no. 4, 139–147 | MR | Zbl

[2] T. Anderson, Vvedenie v mnogomernyi statisticheskii analiz, Fizmatiz, M., 1963 | Zbl

[3] G. Kramer, M. Lidbetter, Statsionarnye sluchainye protsessy. Svoistva vyborochnykh funktsii i ikh primeneniya, Mir, M., 1969 | MR | Zbl

[4] Yu. K. Belyaev, “O chisle peresechenii urovnya gaussovskim sluchainym protsessom”, Teor. veroyatn. i ee prim., 11:1 (1966), 120–128 | MR | Zbl