Geometric process (GP) was introduced by Lam<SUP>[4,5]</SUP>, it is defined as a stochastic process {X <SUB>n </SUB>, n = 1, 2, · · ·} for which there exists a real number a 】 0...Geometric process (GP) was introduced by Lam<SUP>[4,5]</SUP>, it is defined as a stochastic process {X <SUB>n </SUB>, n = 1, 2, · · ·} for which there exists a real number a 】 0, such that {a <SUP>n−1</SUP> X <SUB>n </SUB>, n = 1, 2, · · ·} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for S <SUB>n </SUB>with a 】 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.展开更多
基金the Department of Statistics of the Chinese University of Hong Kong.
文摘Geometric process (GP) was introduced by Lam<SUP>[4,5]</SUP>, it is defined as a stochastic process {X <SUB>n </SUB>, n = 1, 2, · · ·} for which there exists a real number a 】 0, such that {a <SUP>n−1</SUP> X <SUB>n </SUB>, n = 1, 2, · · ·} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for S <SUB>n </SUB>with a 】 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.
