JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Stochastic continuity and approximation

### Tom 121 / 1996

Studia Mathematica 121 (1996), 15-33 DOI: 10.4064/sm-121-1-15-33

#### Streszczenie

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.

#### Autorzy

• Leon Brown
• Bertram M. Schreiber

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek