Optimal Prediction of the Last-Passage Time of a Transient Diffusion

We identify the integrable stopping time \tau_* with minimal L^1-distance to the last-passage time \gamma_z to a given level z>0, for an arbitrary non-negative time-homogeneous transient diffusion X. We demonstrate that \tau_* is in fact the first time that X assumes a value outside a half-open interval [0,r_*). The upper... Show more