Convergence in law of partial sum processes in \(p\)-variation norm

DOI10.1007/s10986-008-9001-0zbMath1226.60039OpenAlexW2020125207MaRDI QIDQ946145

Rimas Norvaiša, Alfredas Račkauskas

Publication date: 22 September 2008

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-008-9001-0

zbMATH Keywords

convergence in lawnonlinear regression\(p\)-variationpartial sum processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (5)

Local depth ⋮ Uniform asymptotic normality of weighted sums of short-memory linear processes ⋮ p-Variation of CUSUM process and testing change in the mean ⋮ Computation of \(p\)-variation ⋮ Uniform asymptotic normality of self-normalized weighted sums of random variables

Cites Work

• Universal Donsker classes and metric entropy
• Fréchet differentiability, \(p\)-variation and uniform Donsker classes
• Limit processes for sequences of partial sums of regression residuals
• Differentiability of six operators on nonsmooth functions and \(p\)-variation. With the collaboration of Jinghua Qian
• The \(p\)-variation of partial sum processes and the empirical process
• Necessary and sufficient condition for the functional central limit theorem in Hölder spaces
• Speed of convergence of classical empirical processes in \(p\)-variation norm
• Weak convergence and empirical processes. With applications to statistics
• Hölderian properties of partial sums of regression residuals
• Sample functions of the Gaussian process
• An inequality of the Hölder type, connected with Stieltjes integration
• A Remark on the Space of Functions of Boundedp-Variation
• Uniform Central Limit Theorems
• Probability for Statisticians
• Real Analysis and Probability
• On Convergence of Stochastic Processes
• Heuristic Approach to the Kolmogorov-Smirnov Theorems
• On certain limit theorems of the theory of probability
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