Moderate and $L^p$ maximal inequalities for diffusion processes and conformal martingales
Probability
2021-11-05 v1
Abstract
The maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the maximal inequalities as special cases. Moreover, we apply our theory to many specific examples, including the Ornstein-Uhlenbeck (OU) process, Brownian motion with drift, reflected Brownian motion with drift, Cox-Ingersoll-Ross process, radial OU process, and Bessel process. The results are further applied to establish the moderate maximal inequalities for some high-dimensional processes, including the complex OU process and general conformal local martingales.
Cite
@article{arxiv.2111.02641,
title = {Moderate and $L^p$ maximal inequalities for diffusion processes and conformal martingales},
author = {Xian Chen and Yong Chen and Mumien Cheng and Chen Jia},
journal= {arXiv preprint arXiv:2111.02641},
year = {2021}
}