Large deviations for the boundary local time of doubly reflected Brownian Motion

Martin Forde, Rohini Kumar, Hongzhong Zhang

We compute a closed-form expression for the moment generating function $\hat{f}(x;\lambda ,\alpha )=\frac{1}{\lambda }{\mathbb{E}}_x(e^{\alpha L_{\tau }})$, where $L_t$ is the local time at zero for standard Brownian…