Stone-Weierstrass theorems for random functions
DOI:
https://doi.org/10.24193/subbmath.2019.2.10Keywords:
Stone-Weierstrass theorem, approximation of random functions, stochastic convergence, random polynomial.Abstract
We present several generalizations of the Stone-Weierstrass theorem concerning the approximation of continuous functions on a compact set by using functions from a subalgebra to the case of random functions and random variables in the space of continuous functions. The continuity of the random functions is allowed to be only with respect to a metric, hence including the case of stochastically continuous random functions. These results could be cornerstones for the general theory of approximation for random functions.
Mathematics Subject Classification (2010): 41A65, 60G07, 60B11.
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