Electronic Communications in Probability

Limiting distribution of the rightmost particle in catalytic branching Brownian motion

Sergey Bocharov and Simon C. Harris

Full-text: Open access

Abstract

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate $\beta \delta _0(\cdot )$, where $\delta _0(\cdot )$ is the Dirac delta function and $\beta $ is some positive constant. We show that the distribution of the rightmost particle centred about $\frac{\beta } {2}t$ converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.

Article information

Source
Electron. Commun. Probab. Volume 21 (2016), paper no. 70, 12 pp.

Dates
Received: 12 May 2016
Accepted: 7 September 2016
First available in Project Euclid: 4 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1475601101

Digital Object Identifier
doi:10.1214/16-ECP22

Zentralblatt MATH identifier
1346.60128

Subjects
Primary: 60J55: Local time and additive functionals 60J65: Brownian motion [See also 58J65] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Brownian motion local time catalytic branching

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bocharov, Sergey; Harris, Simon C. Limiting distribution of the rightmost particle in catalytic branching Brownian motion. Electron. Commun. Probab. 21 (2016), paper no. 70, 12 pp. doi:10.1214/16-ECP22. https://projecteuclid.org/euclid.ecp/1475601101


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References

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