## Electronic Communications in Probability

### Sharp inequality for bounded submartingales and their differential subordinates

#### Abstract

Let $\alpha$ be a fixed number from the interval $[0,1]$. We obtain the sharp probability bounds for the maximal function of the process which is $\alpha$-differentially subordinate to a bounded submartingale. This generalizes the previous results of Burkholder and Hammack.

#### Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 61, 660-675.

Dates
Accepted: 19 December 2008
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465233488

Digital Object Identifier
doi:10.1214/ECP.v13-1433

Mathematical Reviews number (MathSciNet)
MR2466194

Zentralblatt MATH identifier
1196.60074

Subjects
Primary: 60G42: Martingales with discrete parameter
Secondary: 60G46: Martingales and classical analysis

Rights