Approximation of random fields by generalized linear splines
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.
scientific article; zbMATH DE number 1262499