Some Limit Theorems in Geometric
Processes |
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| Authors: | Email author" target="_blank">Yeh?LamEmail author Yao-hui?Zheng Yuan-lin?Zhang |
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| Institution: | (1) Northeastern University at Qinhuangdao, 066004, China;(2) Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong;(3) Department of Mathematics, Xiamen University, Xiamen, 361005, China;(4) Institute of Applied Probability, Sanjiang University, Nanjing, 210018, China;(5) Department of Applied Mathematics, Southeast University, Nanjing, 210018, China;(6) Present address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |
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| Abstract: | Geometric process (GP) was introduced by
Lam4,5], it is defined as a
stochastic process {X
n
, n = 1, 2, · · ·} for which there exists
a real number a > 0, such
that {a
n−1
X
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. |
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| Keywords: | Geometric process new better than used in expectation stochastic order |
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