On extremal distributions and sharp \(L_p\)-bounds for sums of multilinear forms

DOI10.1214/aop/1048516531zbMath1033.60019OpenAlexW2004205467MaRDI QIDQ1394522

Rustam Ibragimov, Shaturgun Sharakhmetov, Victor H. de la Peña

Publication date: 20 March 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1048516531

zbMATH Keywords

stochastic Taylor expansionlong-range dependencenonlinear statisticsmoving average processesdecoupling inequalitiesextremal distributionsautocorrelation processesBurkholder-Rosenthal-type and Khinchin-type inequalitiessums of multilinear forms

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) (L^p)-limit theorems (60F25)

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Cites Work

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• Isoperimetry and integrability of the sum of independent Banach-space valued random variables
• Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
• Random multilinear forms
• Decoupling inequalities for multilinear forms in independent symmetric random variables
• Estimates of moments of infinite-dimensional martingales
• Sharp inequalities for the conditional square function of a martingale
• Decoupling and Khintchine's inequalities for \(U\)-statistics
• Distribution function inequalities for martingales
• On a domination of sums of random variables by sums of conditionally independent ones
• Sharp inequality for randomly stopped sums of independent non-negative random variables
• Order of magnitude bounds for expectations of \(\Delta_2\)-functions of nonnegative random bilinear forms and generalized \(U\)-statistics
• Estimation of moments of sums of independent real random variables
• Limit theorems for functionals of moving averages
• The best constant in the Rosenthal inequality for nonnegative random variables
• Decoupling and domination inequalities with application to Wald's identity for martingales
• Decoupling inequalities for the tail probabilities of multivariate \(U\)- statistics
• Optimum bounds for the distributions of martingales in Banach spaces
• Best constants in martingale version of Rosenthal's inequality
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces
• Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
• Estimates of the Moments of Sums of Independent Random Variables
• О точной константе в неравенстве Розенталя
• Некоторые уточнения вероятностных и моментных неравенств
• The best constants in the Khintchine inequality
• Sharp Square-Function Inequalities for Conditionally Symmetric Martingales
• On the Estimation of Moments of Sums of Independent Random Variables
• On the Behavior of the Constant in a Decoupling Inequality for Martingales
• The Khintchine inequalities and martingale expanding sphere of their action
• Analogues of Khintchine, Marcinkiewicz–Zygmund and Rosenthal Inequalities for Symmetric Statistics
• Inequalities: theory of majorization and its applications
• Exact estimates for moments of random bilinear forms

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