Some Limit Theorems in Geometric Processes

被引：0
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作者：
Yeh Lam
Yao-hui Zheng
Yuan-lin Zhang
机构：
[1] Northeastern University at Qinhuangdao,Department of Statistics and Actuarial Science
[2] University of Hong Kong,Department of Mathematics
[3] Xiamen University,Institute of Applied Probability
[4] Sanjiang University,Department of Applied Mathematics
[5] Southeast University,Department of Statistics and Actuarial Science
[6] The University of Hong Kong,undefined
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2003年 / 19卷 / 3期
关键词：
Geometric process; new better than used in expectation; stochastic order; 60G55; 60K99;
D O I：
10.1007/s10255-003-0115-1
中图分类号：
学科分类号：
摘要：
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n = 1, 2, · · ·} for which there exists a real number a > 0, such that {an−1Xn, 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 Sn 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.
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页码：405 / 416
页数：11
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