Branching random walks in random environment and super-Brownian motion in random environment
arXiv:1304.6140
Abstract
We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr et.al. Each particle performs simple random walk on and branching mechanism depends on the time-space site. The weak limit of this measure valued processes is characterized as a solution to the non-trivial martingale problem and called super-Brownian motions in random environment by L. Mytnik. Moreover, we will show the weak uniqueness of the solutions with some initial condition.
arXiv commentarXiv admin note: substantial text overlap with arXiv:1207.1755