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Some Limit Theorems in Geometric Processes

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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 {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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Author notes

  1. Yeh Lam

    Present address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Authors and Affiliations

  1. Northeastern University at Qinhuangdao, 066004, China

    Yeh Lam

  2. Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong

    Yeh Lam

  3. Department of Mathematics, Xiamen University, Xiamen, 361005, China

    Yao-hui Zheng

  4. Institute of Applied Probability, Sanjiang University, Nanjing, 210018, China

    Yuan-lin Zhang

  5. Department of Applied Mathematics, Southeast University, Nanjing, 210018, China

    Yuan-lin Zhang

Authors
  1. Yeh Lam
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  2. Yao-hui Zheng
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  3. Yuan-lin Zhang
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Correspondence to Yeh Lam.

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Lam, Y., Zheng, Yh. & Zhang, Yl. Some Limit Theorems in Geometric Processes. Acta Mathematicae Applicatae Sinica, English Series, English Series 19, 405–416 (2003). https://doi.org/10.1007/s10255-003-0115-1

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  • DOI: https://doi.org/10.1007/s10255-003-0115-1

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