Abstract
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 give a discrete analogue for the random walk.
Citation
Uwe Rosler. "Unimodality of Passage Times for One-Dimensional Strong Markov Processes." Ann. Probab. 8 (4) 853 - 859, August, 1980. https://doi.org/10.1214/aop/1176994672
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