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

We compute a closed-form expression for the moment generating function fˆ(x;λ,α)=1λEx(eαLτ), where LtLt is the local time at zero for standard Brownian motion with reflecting barriers at 00 and bb, and τ∼Exp(λ) is independent of WW. By analyzing how and where fˆ(x;⋅,α) blows up in λλ, a large-time large deviation principle (LDP) for Lt/tLt/t is established using a Tauberian result and the Gärtner–Ellis Theorem.