§ 02 / martingales

Martingales in Continuous Time

Optional sampling, Doob inequalities, convergence, and applications to Brownian motion.

Explain the core ideas of martingales in continuous time.
Work through definitions and key theorems with KaTeX.
Check understanding with the chapter quiz and simulations.

Section 1 / 8

Martingales in Continuous Time — Overview

The goal of this section is to transfer the most important results for martingales from discrete time to continuous time. As expected, several technical obstacles arise in continuous time that do not occur in discrete time. Most of them can be overcome elegantly by considering martingales with continuous, or more generally right-continuous, paths.

First, we summarize the most important results for martingales in discrete time.