A class of measure-valued branching diffusions in a random medium

Abstract

For any positive integer n, an interacting branching particle system is considered in which particles move in a random medium on at time t. In between branching times, the motion is governed by a singular, degenerate diffusion coefficient; each particle has mass 1/θnand branches at rate , where γ≥ 0 and θ ≥ 2 are fixed constants. As n →∞, the existence, uniqueness, Markovian property, and continuity of the limiting measure-valued processes are investigated