engleski

Direct Largrange - Yen - type interpolation of random processes

We consider the space $L^2(\mathbb R^d ; \Omega($ such that is consisting ffrom $d$-dimensional weka Cram\'er random fields with some conditions on spectral densities. In the paper is shown that the finite, time varying Kotel'nikov-Shannon sum of such that field, which is nonuniformly sampled in the Yen sense, approximates the initial random field in the mean square and almost sure sense with precribed realtive approximation error level. We are focusing o the multidimensional Kotel'nikov-Shannon sampling formula such that remains valid when just finite size sampling knots are deviated from the uniform spacing. Finally, convergence rate estimates are given, oversampling is discussed and an extension is proposed to the $L^\alpha(\mathbb R^d ; \Omega), \alpha \in [0, 2]$.

random fields; function of exponential type; Frech\'et- (semi-) variation; Kadets-Sun-Zhu 1/4-theorem; Kotel'nikov-Shannon sampling formula; Lagrange-Yen interpolator; mean square convergence; truncation error upper bound; weak Cram\'er class random fields

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