Abstract
The article deals with some interpolation representations of random processes with non-equidistance interpolation knots. Research is based on observations of the process and its derivatives of the first, second and third orders at some types of knots and observations of the process and its derivatives of the first and second orders at another types of knots
Highlights
Interpolation representations of a class of random process with non-equidistance interpolation knots are investigated
The interpolation formula that uses the value of the process and its derivatives at the knots of interpolation is proved
For a second type of knots, the interpolation formula includes the value of the process and its derivatives of first and second orders
Summary
1. Introduction Interpolation representations of a class of random process with non-equidistance interpolation knots are investigated. The convergence with probability 1 of the corresponding interpolation series to a random process in any bounded domain of parameter changes is proved. Many problems concerning the construction of a spline approximation as well as a representation of a motion in 3D-modelling with help of interpolation and approximation [6] and the modern theory of signal transmission [7] are based on the Kotel’nikov-Shannon theorem.
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