Convergence of a “Gibbs-Boltzmann” random measure for a typed branching diffusion
The unscaled paths of branching brownian motion
For a set ⊂ [0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within . We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles near the frontier...
Strong law of large numbers for branching diffusions
Let be the branching particle diffusion corresponding to the operator +(2−) on ⊆ℝ (where ≥0 and ≢0). Let denote the generalized principal eigenvalue for the operator + on and assume that it is finite. When >0 and +− satisfies certain spectral theoretical conditions, we prove that the random measure {− } converges almost surely in the vague topology as tends to infinity. This result is motivated...
Survival probabilities for branching Brownian motion with absorption.
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