CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk with a random environment m 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 envi- ronment is supposed to be independent and identically distributed. For A C R, 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.

顾及RMLE的GNSS时序噪声特性及环境负载修正

针对环境负载易对全球卫星导航系统(GNSS)站坐标时序修正前后噪声模型特性及其站速度造成影响的问题,提出一种顾及约束最大似然估计(RMLE)的GNSS时序噪声特性及环境负载修正方法:选用206个连续13a的GNSS站时间序列,采用改进的贝叶斯信息模型估计准则,利用约束最大似然估计(RMLE)方法探讨和分析大气压负载、非海洋潮汐负荷、积雪负载及土壤水负载等环境负载对GNSS时序修正前后噪声模型特性及其站速度的影响。结果表明:经环境负载修正后,GNSS时序中的噪声主要表现为闪烁噪声+白噪声(FNWN)与幂律噪声+白噪声(PLWN),北(N)、东(E)、天(U)3个分量上噪声模型修正前后分别有约19.9%、36.5%、40.8%的噪声模型发生变化,N、E、U分量上分别有96.6%、84.5%、88.3%的测站速度不确定度减小,对垂直速度估计的最大影响可达0.5mm/a;证明环境负载修正能够提高速度估值的精度。