Limiting Distribution of the Rightmost Particle in Catalytic Branching Brownian Motion
| Autor: | Simon R. Harris, Sergey Bocharov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Local time Catalytic branching Binary number Asymptotic distribution Dirac delta function 01 natural sciences 010104 statistics & probability symbols.namesake local time Gumbel distribution Mathematics::Probability FOS: Mathematics 60J65 0101 mathematics Brownian motion Mathematics Mathematical physics 60J80 010102 general mathematics Probability (math.PR) symbols 60J55 catalytic branching Statistics Probability and Uncertainty Martingale (probability theory) Mathematics - Probability |
| Zdroj: | Bocharov, S & Harris, S C 2016, ' Limiting distribution of the rightmost particle in catalytic branching Brownian motion ', Electronic Communications in Probability, vol. 21, Paper no. 70 . https://doi.org/10.1214/16-ECP22 Electron. Commun. Probab. |
| DOI: | 10.48550/arxiv.1603.01600 |
| Popis: | 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 [6] for the degenerate case of catalytic branching. Comment: 12 pages |
| Databáze: | OpenAIRE |
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