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Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin

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  • Rozovsky, Leonid

Abstract

We study the small deviations of [summation operator]j>=1[lambda]jXj and supj>=1[lambda]jXj, where {Xj} are i.i.d. non-negative random variables and 1/[lambda]j tends to [infinity] faster than any power of j. The most interesting conclusions hold if .

Suggested Citation

  • Rozovsky, Leonid, 2009. "Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1495-1500, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1495-1500
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    References listed on IDEAS

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    1. Aurzada, Frank, 2008. "A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2300-2307, October.
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    Cited by:

    1. Rozovsky, Leonid, 2010. "On the behavior of the log Laplace transform of series of weighted non-negative random variables at infinity," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 764-770, May.
    2. Rozovsky, L.V., 2016. "Small deviation probabilities for weighted sum of independent random variables with a common distribution that can decrease at zero fast enough," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 192-200.

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    1. Rozovsky, L.V., 2016. "Small deviation probabilities for weighted sum of independent random variables with a common distribution that can decrease at zero fast enough," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 192-200.
    2. Rozovsky, Leonid, 2010. "On the behavior of the log Laplace transform of series of weighted non-negative random variables at infinity," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 764-770, May.

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