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Czasopismo

1996 | 121 | 1 | 15-33

Tytuł artykułu

Stochastic continuity and approximation

Treść / Zawartość

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.

Czasopismo

Rocznik

Tom

121

Numer

1

Strony

15-33

Daty

wydano
1996
otrzymano
1995-07-06
poprawiono
1996-04-12

Twórcy

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

Bibliografia

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