Accession Number : AD0775941

Title :   Iterates of Markov Operators.

Descriptive Note : Technical rept.,

Corporate Author : ARIZONA STATE UNIV TEMPE DEPT OF MATHEMATICS

Personal Author(s) : Nielson,Gregory M. ; Risenfeld,Richard F. ; Weiss,Neil A.

Report Date : FEB 1974

Pagination or Media Count : 27

Abstract : In the paper the authors consider iterates of Markov operators of the form phi f(x) = the summation from j=0 to m f(j/m) (phi sub j)(x) where the (phi sub j)'s are linearly independent, nonnegative and sum to 1. The authors define the evaluation matrix of phi to be phi* = ((phi sub j)(i/m)) and prove that the iterates of the operator converge in the operator norm if and only if the powers of the evaluation matrix converge. Using results from the theory of Markov chains the authors explicit expressions for the limiting operator when it exists. Finally, the authors apply these results to Bernstein operators and then to B-spline operators. (Modified author abstract)

Descriptors :   *Stochastic processes, *Iterations, Matrices(Mathematics), Splines, Polynomials, Theorems

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE