Martingales

Overview

A martingale is a random process where the best guess (in the expected value sense) of the process at future times is the value of the process now.

Measure Theoretic Definition

Given a Probability space ({% \Omega, F, \mathbb{P} %}), X is a martingale if

• {% X %} is adapted
• {% \mathbb{E}[X] < \infty %}
• {% \mathbb{E}[X_n | F_{n-1}] = X_{n-1} %}