# Branching Brownian motion in strip: survival near criticality

@article{Harris2012BranchingBM,
title={Branching Brownian motion in strip: survival near criticality},
author={Simon Harris and Marion Hesse and Andreas E. Kyprianou},
journal={arXiv: Probability},
year={2012}
}
• Published 6 December 2012
• Mathematics
• arXiv: Probability
We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the…

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## References

SHOWING 1-10 OF 49 REFERENCES

### Survival of Near-Critical Branching Brownian Motion

• Mathematics
• 2011
Consider a system of particles performing branching Brownian motion with negative drift $\mu= \sqrt{2 - \varepsilon}$ and killed upon hitting zero. Initially there is one particle at x>0. Kesten

### The unscaled paths of branching brownian motion

• Mathematics
• 2010
For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the

### A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales

• Mathematics
• 2009
We present a modified formalization of the ‘spine’ change of measure approach for branching diffusions in the spirit of those found in Kyprianou [40] and Lyons et al. [44, 43, 41]. We use our

### Growth of Lévy trees

• Mathematics
• 2005
We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of

### Séminaire de probabilités XLII

• Mathematics
• 2009
Yet another introduction to rough paths.- Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type.- Non-monotone convergence in the quadratic Wasserstein

### Introductory Lectures on Fluctuations of Lévy Processes with Applications

Levy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance

### Local extinction versus local exponential growth for spatial branching processes

• Mathematics
• 2004
Let X be either the branching diffusion corresponding to the operator Lu+β(u2−u) on D⊆ Rd [where β(x)≥0 and β≡0 is bounded from above] or the superprocess corresponding to the operator Lu+βu−αu2 on

### Diffusions, Markov processes, and martingales

• Mathematics
• 1979
This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first,