# A Strong Law of Large Numbers for Super-Critical Branching Brownian Motion with Absorption

@article{Louidor2020ASL, title={A Strong Law of Large Numbers for Super-Critical Branching Brownian Motion with Absorption}, author={Oren Louidor and Santiago Saglietti}, journal={Journal of Statistical Physics}, year={2020} }

We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is well-known that if and only if the branching rate is sufficiently large, then the population survives forever with positive probability. We show that throughout this super-critical regime, the number of particles inside any fixed set normalized by the mean…

## 3 Citations

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We give necessary and sufficient conditions for laws of large numbers to hold in L for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some…

### On laws of large numbers in $L^{2}$ for supercritical branching Markov processes beyond $\lambda $-positivity

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- 2017

We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems…

### Maximal displacement and population growth for branching Brownian motions

- MathematicsIllinois Journal of Mathematics
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We study the maximal displacement and related population for a branching Brownian motion in Euclidean space in terms of the principal eigenvalue of an associated Schr\"odinger type operator. We first…

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