Probabilities of small deviations of the weighted sum of independent random variables with common distribution that decreases at zero not faster than a power

DOI10.1007/s10958-016-2796-zzbMath1341.60021OpenAlexW2300603142MaRDI QIDQ292329

Leonid V. Rozovsky

Publication date: 8 June 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-016-2796-z

zbMATH Keywords

independent random variablesweighted sumssmall deviations

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Limit theorems in probability theory (60F99)

Related Items (2)

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

• Extremes of moving averages of random variables with finite endpoint
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• A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights
• On the lower tail probabilities of some random series
• Lower tail probability estimates for subordinators and nondecreasing random walks
• On small deviations of series of weighted positive random variables
• Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin
• Small deviation probabilities of weighted sums under minimal moment assumptions
• On the lower tail probabilities of some random sequences in \(l_{ p }\)
• 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
• Small deviations of series of independent positive random variables with weights close to exponential
• Small Deviations of Series of Independent Nonnegative Random Variables with Smooth Weights
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