Talks' abstracts > Franceschi Sandro

This talk presents two classical representation results for Brownian motion, known as Lévy's and Pitman's theorems. 

Lévy's theorem shows that reflected Brownian motion can be represented in terms of a standard Brownian motion and its minimum. Pitman's theorem goes further by identifying Brownian motion conditioned to stay positive with a transformation of Brownian motion involving its minimum. 

After briefly introducing the necessary tools from stochastic calculus — including local times, Bessel processes, and Doob's h-transforms — we present these two representation theorems and outline their proofs.