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Asymptotic Behaviors for Random Geometric Series

Author

Listed:
  • Fuqing Gao

    (Wuhan University)

  • Yunshi Gao

    (Wuhan University)

  • Xianjie Xia

    (Wuhan University)

Abstract

In this paper, we consider asymptotic behaviors for random geometric series. We first study the convergence rates in the central limit theorem, i.e., the Berry–Esseen bound and Edgeworth expansions, and precise deviations. Then we define a bounded linear operator from the path space of random walk to the path space of the random geometric series and establish the functional central limit theorem, the functional law of iterated logarithm, and functional large deviation principles for the random geometric series.

Suggested Citation

  • Fuqing Gao & Yunshi Gao & Xianjie Xia, 2024. "Asymptotic Behaviors for Random Geometric Series," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2818-2842, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-024-01327-3
    DOI: 10.1007/s10959-024-01327-3
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    References listed on IDEAS

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    1. Stoica, George, 2003. "Functional local law of the iterated logarithm for geometrically weighted random series," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 71-77, March.
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