## Abstract

We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well known that there exists a critical drift which separates those processes which die out almost surely from those which survive with positive probability. In this work, we consider lower-order corrections to the critical drift which ensures a nonnegative, bounded expected number of particles and convergence of this expectation to a limiting nonnegative number which is positive for some initial data. In particular, we show that the average number of particles stabilizes at the convergence rate O(log(t)/t) if and only if the multiplicative factor of the O(t^{-1/2}) correction term is 3√πt^{-1/2}. Otherwise, the convergence rate is O(1/√t). We point out some connections between this work and recent work investigating the expansion of the front location for the initial value problem in Fisher-KPP.

Original language | English (US) |
---|---|

Pages (from-to) | 973-985 |

Number of pages | 13 |

Journal | Communications in Mathematical Sciences |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - 2016 |

Externally published | Yes |

## Keywords

- Absorption
- Bramson correction
- Branching brownian motion
- Delay
- Fisher-KPP
- Population dynamics
- Selection models

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics