Branching diffusions, superdiffusions and random media.
Quenched law of large numbers for branching brownian motion in a random medium
We study a spatial branching model, where the underlying motion is -dimensional (≥1) brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed . The main result of this paper is the quenched law of large numbers for the population for all ≥1. We also show that the branching brownian motion with mild obstacles than ordinary branching brownian motion by giving an upper estimate on its speed. When the underlying motion is an arbitrary diffusion...
Law of large numbers for superdiffusions : the non-ergodic case
In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. , we prove the analog of the Watanabe–Biggins LLN for super-brownian motion.
Law of large numbers for a class of superdiffusions
The compact support property for measure-valued processes
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...
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