1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China 2. School of Science, Beijing Technology and Business University, Beijing 100048, China 3. College of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha 410004, China 4. Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France
We consider a branching random walk on R with a random environment in time (denoted by ξ). Let Zn be the counting measure of particles of generation n, and let Z ?n(t) be its Laplace transform. We show the convergence of the free energy n-1logZ ?n(t), large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Z ?n(t)/E[Z ?n(t)|ξ].
. [J]. Frontiers of Mathematics in China, 2014, 9(4): 835-842.
Chunmao HUANG,Xingang LIANG,Quansheng LIU. Branching random walks with random environments in time. Front. Math. China, 2014, 9(4): 835-842.
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