Fluctuations of the empirical quantiles of independent Brownian motions

DOI10.1016/j.spa.2010.11.012zbMath1230.60022arXiv0812.4102OpenAlexW2085549668MaRDI QIDQ550149

Jason Swanson

Publication date: 8 July 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.4102

zbMATH Keywords

order statisticsfractional Brownian motionquantile processfluctuations weak convergencequartic variation

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Brownian motion (60J65) Sample path properties (60G17) Self-similar stochastic processes (60G18)

Related Items (6)

Central limit theorem for a Stratonovich integral with Malliavin calculus ⋮ Limit Theorems for Quantile and Depth Regions for Stochastic Processes ⋮ A CLT for empirical processes involving time-dependent data ⋮ Variance Estimation for Fractional Brownian Motions with Fixed Hurst Parameters ⋮ Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes ⋮ Empirical quantile central limit theorems for some self-similar processes

Cites Work

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• The motion of a tagged particle in the simple symmetric exclusion system on Z
• Sub-fractional Brownian motion and its relation to occupation times
• Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks
• A change of variable formula with Itô correction term
• Weak convergence of the scaled median of independent Brownian motions
• Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion
• Variations of the solution to a stochastic heat equation
• On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion
• Space-Time Current Process for Independent Random Walks in One Dimension
• Asymptotics of particle trajectories in infinite one-dimensional systems with collisions
• Limit theorems for the motion of a Poisson system of independent Markovian particles with high density
• The Curious History of Faa di Bruno's Formula
• Diffusion with “collisions” between particles

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