The Annals of Probability

Distribution Function Inequalities for Martingales

D. L. Burkholder

Full-text: Open access

Abstract

This is a guide to some recent work in the theory of martingale inequalities. Methods are simplified; some new proofs are given. A number of new results are also included.

Article information

Source
Ann. Probab., Volume 1, Number 1 (1973), 19-42.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176997023

Digital Object Identifier
doi:10.1214/aop/1176997023

Mathematical Reviews number (MathSciNet)
MR365692

Zentralblatt MATH identifier
0301.60035

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 60H05: Stochastic integrals 31A05: Harmonic, subharmonic, superharmonic functions 31B05: Harmonic, subharmonic, superharmonic functions

Keywords
Martingale stopping time maximal function square function quadratic variation Brownian motion Ito integral harmonic function distribution function inequality $\phi inequality

Citation

Burkholder, D. L. Distribution Function Inequalities for Martingales. Ann. Probab. 1 (1973), no. 1, 19--42. doi:10.1214/aop/1176997023. https://projecteuclid.org/euclid.aop/1176997023


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