Iterates of Markov Operators.
ARIZONA STATE UNIV TEMPE DEPT OF MATHEMATICS
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In the paper the authors consider iterates of Markov operators of the form phi fx the summation from j0 to m fjm phi sub jx where the phi sub js are linearly independent, nonnegative and sum to 1. The authors define the evaluation matrix of phi to be phi phi sub jim 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
- Statistics and Probability