Predicting the Last Zero of Brownian Motion with Drift

J. du Toit, G. Peskir, A. N. Shiryaev

Given a standard Brownian motion $B^{\mu }=(B_t^{\mu }{)}_{0\le t\le T}$ with drift $\mu \in IR$ and letting $g$ denote the last zero of $B^{\mu }$ before $T$, we consider the optimal prediction probl…