Stochastic continuity and approximation

Leon Brown; Bertram Schreiber

Studia Mathematica (1996)

  • Volume: 121, Issue: 1, page 15-33
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Brown, Leon, and Schreiber, Bertram. "Stochastic continuity and approximation." Studia Mathematica 121.1 (1996): 15-33. <http://eudml.org/doc/216339>.

@article{Brown1996,
abstract = {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.},
author = {Brown, Leon, Schreiber, Bertram},
journal = {Studia Mathematica},
keywords = {stochastic processes which are continuous in probability; rational approximation; continuity in probability},
language = {eng},
number = {1},
pages = {15-33},
title = {Stochastic continuity and approximation},
url = {http://eudml.org/doc/216339},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Brown, Leon
AU - Schreiber, Bertram
TI - Stochastic continuity and approximation
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 1
SP - 15
EP - 33
AB - 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.
LA - eng
KW - stochastic processes which are continuous in probability; rational approximation; continuity in probability
UR - http://eudml.org/doc/216339
ER -

References

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