Electronic Journal of Probability

Fine asymptotics for the consistent maximal displacement of branching Brownian motion

Matthew Roberts

Full-text: Open access

Abstract

It is well-known that the maximal particle in a branching Brownian motion sits near $\sqrt2 t - \frac{3}{2\sqrt2}\log t$ at time $t$. One may then ask about the paths of particles near the frontier: how close can they stay to this critical curve? Two different approaches to this question have been developed. We improve upon the best-known bounds in each case, revealing new qualitative features including marked differences between the two approaches.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 28, 26 pp.

Dates
Accepted: 13 March 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067134

Digital Object Identifier
doi:10.1214/EJP.v20-2912

Mathematical Reviews number (MathSciNet)
MR3325098

Zentralblatt MATH identifier
1320.60145

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching Brownian motion consistent minimal displacement survival probability growth rate

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Roberts, Matthew. Fine asymptotics for the consistent maximal displacement of branching Brownian motion. Electron. J. Probab. 20 (2015), paper no. 28, 26 pp. doi:10.1214/EJP.v20-2912. https://projecteuclid.org/euclid.ejp/1465067134


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