## The Annals of Probability

### Unimodality of Passage Times for One-Dimensional Strong Markov Processes

Uwe Rosler

#### 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.

#### Article information

Source
Ann. Probab., Volume 8, Number 4 (1980), 853-859.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994672

Digital Object Identifier
doi:10.1214/aop/1176994672

Mathematical Reviews number (MathSciNet)
MR577322

Zentralblatt MATH identifier
0446.60025

JSTOR