Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Yaglom-type limit theorems for branching Brownian motion with absorption

Abstract : We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards the origin so that the process eventually goes extinct with probability one. We establish precise asymptotics for the probability that the process survives for a large time t, building on previous results by Kesten (1978) and Berestycki, Berestycki, and Schweinsberg (2014). We also prove a Yaglom-type limit theorem for the behavior of the process conditioned to survive for an unusually long time, providing an essentially complete answer to a question first addressed by Kesten (1978). An important tool in the proofs of these results is the convergence of a certain observable to a continuous state branching process. Our proofs incorporate new ideas which might be of use in other branching models.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02981261
Contributor : Pascal Maillard <>
Submitted on : Tuesday, July 20, 2021 - 12:10:06 PM
Last modification on : Wednesday, July 28, 2021 - 6:33:56 PM

Files

critical_BBM_absorption_v43.pd...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02981261, version 2
  • ARXIV : 2010.16133

Citation

Pascal Maillard, Jason Schweinsberg. Yaglom-type limit theorems for branching Brownian motion with absorption. 2021. ⟨hal-02981261v2⟩

Share

Metrics

Record views

6

Files downloads

8