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On the distribution of the maxima of partial sums

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  • Sgibnev, M. S.

Abstract

Let Xn, N = 1, 2, ..., be independent identically distributed random variables with common distribution function F and let S0 = 0, Sn = [summation operator]k = 1n Xk, N = 1, 2,.... We show that in a wide range of cases the distribution of Mn = max0 [less-than-or-equals, slant] k [less-than-or-equals, slant] n Sk inherits the asymptotic properties of F.

Suggested Citation

  • Sgibnev, M. S., 1996. "On the distribution of the maxima of partial sums," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 235-238, July.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:3:p:235-238
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    Cited by:

    1. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2014. "Closure property and maximum of randomly weighted sums with heavy-tailed increments," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 162-170.
    2. Jiang, Tao & Wang, Yuebao & Cui, Zhaolei & Chen, Yuxin, 2019. "On the almost decrease of a subexponential density," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 71-79.
    3. Zhu, Chun-hua & Gao, Qi-bing, 2008. "The uniform approximation of the tail probability of the randomly weighted sums of subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2552-2558, October.

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