The Annals of Probability

Unimodality of Passage Times for One-Dimensional Strong Markov Processes

Uwe Rosler

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Birth-death processes diffusion unimodality variation diminishing property

Citation

Rosler, Uwe. Unimodality of Passage Times for One-Dimensional Strong Markov Processes. Ann. Probab. 8 (1980), no. 4, 853--859. doi:10.1214/aop/1176994672. https://projecteuclid.org/euclid.aop/1176994672


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