Unimodality of Passage Times for One-Dimensional Strong Markov Processes
Unimodality of Passage Times for One-Dimensional Strong Markov Processes
Let $\tau_x$ be the first passage time of $x$ for a diffusion or birth-death process. If one starts in a reflecting state, say 0, then the distribution $P_0(\tau_x \leqslant \cdot)$ is strongly unimodal. Here we show for an arbitrary state 0 the distribution $P_0(\tau_x \leqslant \cdot)$ is unimodal. Further we …