Small Deviations of Probabilities for Weighted Sum of Independent Positive Random Variables with a Common Distribution That Decreases at Zero Not Faster than a Power

DOI10.1137/S0040585X97T987545zbMath1334.60050MaRDI QIDQ2790686

Leonid V. Rozovsky

Publication date: 8 March 2016

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

zbMATH Keywords

weighted sumssmall deviationsslowly varying functionsindependent positive random variables

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Limit theorems in probability theory (60F99)

Related Items (5)

Probabilities of small deviations of the weighted sum of independent random variables with common distribution that decreases at zero not faster than a power ⋮ Small deviation probabilities for weighted sum of independent random variables with a common distribution that can decrease at zero fast enough ⋮ Small deviation probabilities of a sum of independent positive random variables, the common distribution of which decreases at zero not faster than exponential function ⋮ On the history of St. Petersburg school of probability and mathematical statistics. II: Random processes and dependent variables ⋮ Small Deviation Probabilities for a Weighted Sum of Independent Positive Random Variables with Common Distribution Function That Can Decrease at Zero Fast Enough

Cites Work

• On the lower tail probabilities of some random series
• Remarks on a link between the Laplace transform and distribution function of a nonnegative random variable
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