Convergence of martingale and moderate deviations for a branching random walk with a random environment in time

2015/04/06 by Xiaoqiang Wang, Wang, Xiaoqiang, Chunmao Huang +1 · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1504.01181

arxiv created 2015/04/06 · arxiv updated 2015/04/07

Abstract

We consider a branching random walk on ℝ with a stationary and ergodic environment ξ=(ξ_n) indexed by time n∈ℕ. Let Z_n be the counting measure of particles of generation n and Z_n(t)=∫ e^txZ_n(dx) be its Laplace transform. We show the L^p convergence rate and the uniform convergence of the martingale Z_n(t)/\mathbb E[ Z_n(t)|ξ], and establish a moderate deviation principle for the measures Z_n.

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• Exact convergence rates in central limit theorems for a branching random walk with a random environment in time

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