A Cluster Expansion Proof That The Stochastic Exponential Of A Brownian Motion Is A Martingale

Steven D Miller

Let $\psi :{\mathbb{R}}^{+}\to {\mathbb{R}}^{+}$ be a smooth and continuous real function and $\psi \in {\mathrm{L}}^2({\mathbb{R}}^{+})$. Let $B(t)$ be a standard Brownian motion define…