Asymptotic properties of supercritical branching processes in random environments

作者：Li, Yingqiu; Liu, Quansheng^*; Gao, Zhiqiang; Wang, Hesong

来源：Frontiers of Mathematics in China, 2014, 9(4): 737-751.

DOI：10.1007/s11464-014-0397-z

• Branching process
• random environment
• large deviation
• moderate deviation
• central limit theorem
• moment
• weighted moment
• convergence rate

We consider a supercritical branching process (Z(n)) in an independent and identically distributed random environment xi, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale W-n = Z(n)/E[Z(n)vertical bar xi], the convergence rates of W - W-n (by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in L-p, and the convergence in probability), and limit theorems (such as central limit theorems, moderate and large deviations principles) on (log Z(n)).

• 出版日期2014-8
• 单位北京师范大学; 长沙理工大学