Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 405–416

# Some Limit Theorems in Geometric Processes

• Yeh Lam
• Yao-hui Zheng
• Yuan-lin Zhang
Original papers

## Abstract

Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {X n , n = 1, 2, · · ·} for which there exists a real number a > 0, such that {an−1X n , 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 n 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.

## Keywords

Geometric process new better than used in expectation stochastic order

60G55 60K99

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