Lecture notes on martingale inequalities

TL;DR

This paper discusses techniques for establishing $L^p$ bounds for martingales, with applications to Itô integration and rough path theory, providing foundational methods for stochastic analysis.

Contribution

It introduces new techniques for proving $L^p$ estimates for martingales, applicable to Itô integration and rough paths, enhancing analytical tools in stochastic calculus.

Findings

Developed methods for $L^p$ estimates of martingales

Applied techniques to Itô integration

Extended results to rough path analysis

Abstract

We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.