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Central limit theorems for a branching random walk with a random environment in time |
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| Authors: | Zhiqiang GAO Quansheng LIU Hesong WANG |
| Affiliation: | 1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;2. Univ. Bretagne-Sud, CNRS UMR 6205, LMBA, Campus de Tohannic, F-56000 Vannes, France;3. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China;4. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China |
| Abstract: | We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be independent and identically distributed. For A ?, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization. |
| Keywords: | Branching random walk random environment in time central limit theorems |
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