Geodesic
On non-parametric models of multidimensional non-inertial processes with dependent input variables
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 514-521.

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The problem of identification of multidimensional non-inertial systems with delay is considered. Components of the input vector are stochastically related, and this relationship is unknown a priori. Such processes have "tubular" structure in the space of the input and output variables. In this situation methods of identification theory of non-inertial systems are not applicable. In general, it is not known a priori whether the process has "tubular" structure or not. To clear up this question the problem of estimation of the volume of a subdomain where "tubular" process takes place is considered. The initial data for this problem follows from the measurement of input-output variables. An algorithm for estimating the volume of the "tubular" subdomain in relation to the volume of the investigated process is suggested. The volume of the investigated process is always known from a priori information or production schedules. Numerical experiments are carried out with the use of the method of statistical modeling. They show high effectiveness of the proposed algorithm.
Keywords: non-parametric modeling, non-inertial processes with delay, indicator function, H-process. 
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Alexander V. Medvedev; Ekaterina A. Chzhan. On non-parametric models of multidimensional non-inertial processes with dependent input variables. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 514-521. http://geodesic.mathdoc.fr/item/JSFU_2017_10_4_a12/

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