## Illinois Journal of Mathematics

### On the $L^{1}$-behavior of the maximal operator for the class of martingales adapted to a given filtration

#### Abstract

We study the boundedness in $L^{1}$ of the maximal operator of the class of martingales for a fixed increasing or decreasing filtration. We obtain necessary and sufficient conditions for several classes of martingales.

#### Article information

Source
Illinois J. Math., Volume 43, Issue 3 (1999), 568-581.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.ijm/1255985111

Digital Object Identifier
doi:10.1215/ijm/1255985111

Mathematical Reviews number (MathSciNet)
MR1700610

Zentralblatt MATH identifier
0984.60042

Subjects
Primary: 60G42: Martingales with discrete parameter

#### Citation

Bellow, Alexandra; Krengel, Ulrich. On the $L^{1}$-behavior of the maximal operator for the class of martingales adapted to a given filtration. Illinois J. Math. 43 (1999), no. 3, 568--581. doi:10.1215/ijm/1255985111. https://projecteuclid.org/euclid.ijm/1255985111