Electronic Journal of Probability

Critical branching Brownian motion with killing

Steven Lalley and Bowei Zheng

Full-text: Open access

Abstract

We obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0. We also obtain sharp asymptotic formulas for the tail probabilities of the number of particles killed at 0. In the special case of double-or-nothing branching, we give exact formulas for both the hitting probabilities, in terms of elliptic functions, and the distribution of the number of killed particles.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 118, 29 pp.

Dates
Received: 5 August 2015
Accepted: 4 November 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067224

Digital Object Identifier
doi:10.1214/EJP.v20-4466

Mathematical Reviews number (MathSciNet)
MR3425538

Zentralblatt MATH identifier
1328.60196

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J15 34M35: Singularities, monodromy, local behavior of solutions, normal forms

Keywords
Branching Brownian motion barrier power law Weierstrass elliptic function singularity analysis

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

Citation

Lalley, Steven; Zheng, Bowei. Critical branching Brownian motion with killing. Electron. J. Probab. 20 (2015), paper no. 118, 29 pp. doi:10.1214/EJP.v20-4466. https://projecteuclid.org/euclid.ejp/1465067224


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