RESEARCH IN THE INTERPOLATION REPRESENTATIONS OF STOCHASTIC PROCESSES IN THE TWO TYPES OF INTERPOLATION KNOTS

Ganna Verovkina

Abstract


The article deals with some interpolation representations of stochastic processes with non-equidistance interpolation knots. Research is based on observations of the process and its derivatives of the first and second orders at some types of knots and observations of the process and its derivatives of the first orders at other types of knots. The necessary results from the theory of entire functions of complex variable are formulated. The function bounded on any bounded region of the complex plane is considered. The estimate of the residual of the interpolation series is obtained. The interpolation formula that uses the value of the process and its derivatives at the knots of interpolation is proved. Considering the separability of the process and the convergence of a row that the interpolation row converges to the stochastic process uniformly over in any bounded area of changing of parameter is obtained. The main purpose of this article is the obtained convergence with probability 1 of the corresponding interpolation series to a stochastic process in any bounded domain of changes of parameter. Obtained results may be applied in the modern theory of information transmission.


Keywords


stochastic process; interpolation representation; series; non-equidistance interpolation knots; separability; convergence with probability 1

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DOI: http://dx.doi.org/10.21303/2461-4262.2017.00296

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ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)