Stochastic continuity and approximation
Studia Mathematica, Tome 121 (1996) no. 1, pp. 15-33
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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},
publisher = {mathdoc},
volume = {121},
number = {1},
year = {1996},
doi = {10.4064/sm-121-1-15-33},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-15-33/}
}
TY - JOUR AU - Leon Brown AU - Bertram M. Schreiber TI - Stochastic continuity and approximation JO - Studia Mathematica PY - 1996 SP - 15 EP - 33 VL - 121 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-15-33/ DO - 10.4064/sm-121-1-15-33 LA - en ID - 10_4064_sm_121_1_15_33 ER -
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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