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

Abstract

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 motion with reflecting barriers at $0$ and $b$, and $\tau \sim \mathrm{Exp}(\lambda )$ is independent of $W$. By analyzing how and where $\hat{f}(x;\cdot ,\alpha )$ blows up in $\lambda$, a large-time large deviation principle (LDP) for $L_t/t$ is established using a Tauberian result and the Gärtner-Ellis Theorem.

7 pages

References in corpus (1)

• Long Horizons, High Risk Aversion, and Endogeneous Spreads

Cited by in corpus (4)

• Dynamical large deviations of reflected diffusions
• Large deviations of currents in diffusions with reflective boundaries
• Local time of an Ornstein-Uhlenbeck particle
• Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential