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Article Dans Une Revue Frontiers of Mathematics in China Année : 2014

Branching random walks with random environments in time

Résumé

We consider a branching random walk on $\mathbb{R}$ with a random environment in time (denoted by $\xi$). Let $Z_n$ be the counting measure of particles of generation $n$ and $\tilde Z_n (t)$ be its Laplace transform.We show the convergence of the free energy $ n^{-1}{\log \tilde Z_n(t)}$, large deviation principles and central limit theorems for the sequence of measures $\{Z_n\}$, and a necessary and sufficient condition for the existence of moments of the limit of the martingale ${\tilde Z_n(t)}/{\mathbb E[\tilde Z_n(t)|\xi]}$.
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Dates et versions

hal-01095074 , version 1 (15-12-2014)

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Chunmao Huang, Xingang Liang, Quansheng Liu. Branching random walks with random environments in time. Frontiers of Mathematics in China, 2014, 9 (4), pp.835-842. ⟨10.1007/s11464-014-0407-1⟩. ⟨hal-01095074⟩
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