# The number of absorbed individuals in branching Brownian motion with a barrier

@article{Maillard2010TheNO,
title={The number of absorbed individuals in branching Brownian motion with a barrier},
author={Pascal Maillard},
journal={arXiv: Probability},
year={2010}
}

### Total progeny in killed branching random walk

• Mathematics
• 2009
We consider a branching random walk for which the maximum position of a particle in the n’th generation, Rn, has zero speed on the linear scale: Rn/n → 0 as n → ∞. We further remove (“kill”) any

### Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case

• Mathematics
Electronic Communications in Probability
• 2022
The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time 0 . The particle

## References

SHOWING 1-10 OF 28 REFERENCES

### Total progeny in killed branching random walk

• Mathematics
• 2009
We consider a branching random walk for which the maximum position of a particle in the n’th generation, Rn, has zero speed on the linear scale: Rn/n → 0 as n → ∞. We further remove (“kill”) any

### Measure change in multitype branching

• Mathematics
• 2004
The Kesten-Stigum theorem for the one-type Galton-Watson process gives necessary and sufficient conditions for mean convergence of the martingale formed by the population size normed by its

### Handbook of Brownian Motion - Facts and Formulae (Second Edition)

• Mathematics
• 2003
Brownian motion as well as other diffusion processes play a meaningful role in stochastic analysis. They are very important from theoretical point of view and very useful in applications. Diffusions

### Tail asymptotics for the total progeny of the critical killed branching random walk

We consider a branching random walk on (cid:82) with a killing barrier at zero. At criticality, the process becomes eventually extinct, and the total progeny Z is therefore ﬁnite. We show that P ( Z

### Multiplicative Martingales for Spatial Branching Processes

Out of simplicity, we restrict ourselves to consider the dyadic brownian branching process (Nt, t ∈ R+) on the real line. By definition of this process, its particles perform independent brownian

### Conceptual proofs of L log L criteria for mean behavior of branching processes

• Mathematics
• 1995
The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases,

### Handbook of Brownian Motion - Facts and Formulae

• Mathematics
• 1996
I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to