ALMOST SURE CENTRAL LIMIT THEOREM FOR BRANCHING RANDOM WALKS IN RANDOM ENVIRONMENT

作者：Nakashima Makoto^*

来源：Annals of Applied Probability, 2011, 21(1): 351-373.

DOI：10.1214/10-AAP699

• Branching random walk
• random environment
• central limit theorem
• linear stochastic evolutions
• phase transition

We consider the branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When d >= 3 and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.

• 出版日期2011-2