The paper presents estimates of small deviation probabilities of the sum \( {\displaystyle \sum_{j\ge 1}{\leftthreetimes}_j{X}_j} \) , where {⋋j} are positive numbers and {Xj} are i.i.d. positive random variables satisfying weak restrictions at zero and infinity. Bibliography: 16 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 178–185.
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Rozovsky, L.V. Probabilities of Small Deviations of the Weighted Sum of Independent Random Variables with Common Distribution That Decreases at Zero Not Faster Than a Power. J Math Sci 214, 540–545 (2016). https://doi.org/10.1007/s10958-016-2796-z
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DOI: https://doi.org/10.1007/s10958-016-2796-z