Decomposing the Branching Brownian Path
Decomposing the Branching Brownian Path
We consider a real-valued branching Brownian motion where particles are killed at rate $\mu$ and split at rate $\lambda \leq \mu$ into two independent offspring particles. The process dies out almost surely, so it reaches some lowest level. We prove a decomposition of the branching Brownian path at its minimum. …