Stochastic continuity and approximation
Studia Mathematica, Tome 121 (1996) no. 1, pp. 15-33
This work is concerned with the study of stochastic processes which are continuous in probability, over various parameter spaces, from the point of view of approximation and extension. A stochastic version of the classical theorem of Mergelyan on polynomial approximation is shown to be valid for subsets of the plane whose boundaries are sets of rational approximation. In a similar vein, one can obtain a version in the context of continuity in probability of the theorem of Arakelyan on the uniform approximation of continuous functions on a closed set by entire functions. Locally bounded processes continuous in probability are characterized via operators from $L^1$-spaces to spaces of continuous functions. This characterization is utilized in a discussion of the problem of extension of the parameter space.
@article{10_4064_sm_121_1_15_33,
author = {Leon Brown and Bertram M. Schreiber},
title = {Stochastic continuity and approximation},
journal = {Studia Mathematica},
pages = {15--33},
year = {1996},
volume = {121},
number = {1},
doi = {10.4064/sm-121-1-15-33},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-15-33/}
}
Leon Brown; Bertram M. Schreiber. Stochastic continuity and approximation. Studia Mathematica, Tome 121 (1996) no. 1, pp. 15-33. doi: 10.4064/sm-121-1-15-33
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