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arXiv · 2003.14301

Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration

Sorin G. Gal·Constantin Niculescu
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Abstract

Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order $p\ge1$ with a quantitative estimate, of the multivariate Bernstein polynomials associated to a random function. Applications to quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

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Sorin G. Gal, Constantin Niculescu. 2020-03-30. Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration. https://arxiv.org/abs/2003.14301

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