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On the distribution of the maxima of partial sums

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  • Sgibnev, M. S.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 28 (1996)
    Issue (Month): 3 (July)
    Pages: 235-238

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    Handle: RePEc:eee:stapro:v:28:y:1996:i:3:p:235-238

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    Related research

    Keywords: Maxima of partial sums Tail behaviour Densities Subexponential distributions Regular variation;

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    Cited by:
    1. 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.
    2. 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.

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