Lévy's martingale characterization and reflection principle of G-Brownian motion

In this paper, by a new kind of discrete product space method for martingales, we obtain Lévy's martingale characterization of G-Brownian motion without the nondegenerate condition. Based on this characterization, we prove the reflection principle of G-Brownian motion. Furthermore, we use Krylo...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 480; no. 2; p. 123436
Main Authors Hu, Mingshang, Ji, Xiaojun, Liu, Guomin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.12.2019
Subjects
G-Brownian motion
G-expectation
Martingale characterization
Reflection principle
G-expectation
Martingale characterization
Reflection principle
G-Brownian motion
Online AccessGet full text

Cover

More Information
Summary:In this paper, by a new kind of discrete product space method for martingales, we obtain Lévy's martingale characterization of G-Brownian motion without the nondegenerate condition. Based on this characterization, we prove the reflection principle of G-Brownian motion. Furthermore, we use Krylov's estimate to get the reflection principle of the general G˜-Brownian motion.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123436