THE INTERPOLATION REPRESENTATION OF SOME KINDS OF RANDOM FIELDS
Journal Title: Science Review - Year 2018, Vol 1, Issue 3
Abstract
Paper deals with some interpolation representations of random fields with regular pass of interpolation knots. Research is based on observations of the process and its derivatives of the first, second, third and fourth orders. 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 random field the interpolation row converges to the random field uniformly over in any bounded area of changing of parameter is obtained. The main purpose of our work is the obtained convergence with probability 1 of the corresponding interpolation series to the random field in any bounded domain of changes of parameter. Obtained results may be applied in the modern theory of information transmission.
Authors and Affiliations
Ganna Verovkina
Keywords
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