Stochastic continuity and approximation

• Autorzy: Leon Brown , Bertram M. Schreiber
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30E10: Approximation in the complex domain
• 47B07: Operators defined by compactness properties
• 60G17: Sample path properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 1
• Strony: 15-33

Daty

wydano

1996

otrzymano

1995-07-06

poprawiono

1996-04-12

Twórcy

autor

Leon Brown

• Department of Mathematics, Wayne State University, Detroit, Michigan 48202, U.S.A.,

autor

Bertram M. Schreiber

• Department of Mathematics, Wayne State University, Detroit, Michigan 48202, U.S.A.,

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