Approximation of random fields by generalized linear splines

We consider the problem of 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; it is shown that even in the simplest case of approximating a stochastic process by generalized linear splines, the tail of the distribution of the approximation error normalized in an appropriate way decreases exponentially. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 690–696, May, 1998.