Martingales and Brownian Motion: Reflection Principle

This lecture introduces the reflection principle in the context of martingales and Brownian motion, explaining how to simulate small group interactions in virtual classrooms. The instructor demonstrates the calculation of probabilities related to the maximum position reached by Brownian motion at different instants, using the reflection principle to simplify the calculations. The lecture also covers the first passage time of Brownian motion to a specified level, providing insights into the density function and the distribution function. The session includes a detailed explanation of the mathematical derivations involved in these calculations, with a focus on understanding the principles behind the reflection method.