Critical branching Brownian motion with absorption: survival probability
We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of {Mathematical expression}. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2014
|
| Summary: | We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of {Mathematical expression}. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time {Mathematical expression}. These bounds improve upon results of Kesten (Stoch Process 7:9-47, 1978), and partially confirm nonrigorous predictions of Derrida and Simon (EPL 78:60006, 2007). © 2013 Springer-Verlag Berlin Heidelberg. |
|---|