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On Small Deviations of Series of Weighted Random Variables

Author

Listed:
  • A. A. Borovkov

    (Sobolev Institute of Mathematics)

  • P. S. Ruzankin

    (Sobolev Institute of Mathematics)

Abstract

Let ξ,ξ 1,ξ 2,… be positive i.i.d. random variables, S=∑ j=1 ∞ a(j)ξ j , where the coefficients a(j)≥0 are such that P(S 0, where γ=1/(β−1), (ii) −ln P(ξ 0, where γ=1/(β−1), (iii) {a(j)} decreases faster than any power of j, and P(ξ

Suggested Citation

  • A. A. Borovkov & P. S. Ruzankin, 2008. "On Small Deviations of Series of Weighted Random Variables," Journal of Theoretical Probability, Springer, vol. 21(3), pages 628-649, September.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-007-0130-x
    DOI: 10.1007/s10959-007-0130-x
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    References listed on IDEAS

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    1. Frank Aurzada, 2007. "On the Lower Tail Probabilities of Some Random Sequences in l p," Journal of Theoretical Probability, Springer, vol. 20(4), pages 843-858, December.
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    Cited by:

    1. Frank Aurzada & Fuchang Gao & Thomas Kühn & Wenbo V. Li & Qi-Man Shao, 2013. "Small Deviations for a Family of Smooth Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 26(1), pages 153-168, March.
    2. Seok Young Hong & Oliver Linton, 2016. "Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of in finite order," CeMMAP working papers 53/16, Institute for Fiscal Studies.

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