Approximation of random fields by generalized linear splines
type: Item
instance of: scholarly article
title: Approximation of random fields by generalized linear splines
zbMATH Open document ID: 0913.62091
DOI: 10.1007/BF02312841
author: S. A. Egishyants
author: E. I. Ostrovskij
published in: Mathematical Notes
publication date: 1999-06-10T00:00:00Z
review text: The paper considers a problem frequently met in practice: reconstructing stochastic processes or stochastic fields from their known values on a finite grid. This problem is stated and solved in a sufficiently general setting, obtaining practically important upper estimates for the error distribution arising when the stochastic field is approximated by generalized linear splines. Even in this simplest case, the tail of the distribution for the approximation error, normalized in an approximate way, is proved to decrease exponentially. A lower estimate is also obtained, the results providing a good basis of the statistical analysis for reconstructing stochastic processes from their known realizations on a finite grid, as well as by the Monte Carlo method.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 62L20
zbMATH DE Number: 1262499
zbMATH Keywords: approximation of random fields
zbMATH Keywords: reconstruction of stochastic processes
zbMATH Keywords: generalized linear splines
MaRDI profile type: Publication
cites work: Q5580054
cites work: Q3911932
cites work: Limit Theorems for the Maximum Term in Stationary Sequences
cites work: Extremes and related properties of random sequences and processes
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description: scientific article; zbMATH DE number 1262499