Open Access
August, 1980 Unimodality of Passage Times for One-Dimensional Strong Markov Processes
Uwe Rosler
Ann. Probab. 8(4): 853-859 (August, 1980). DOI: 10.1214/aop/1176994672


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.


Download Citation

Uwe Rosler. "Unimodality of Passage Times for One-Dimensional Strong Markov Processes." Ann. Probab. 8 (4) 853 - 859, August, 1980.


Published: August, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0446.60025
MathSciNet: MR577322
Digital Object Identifier: 10.1214/aop/1176994672

Primary: 60G40

Keywords: birth-death processes , diffusion , Unimodality , variation diminishing property

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 4 • August, 1980
Back to Top