Weak convergence of the scaled median of independent Brownian motions

DOI10.1007/s00440-006-0024-3zbMath1116.60010arXivmath/0507524OpenAlexW3104276818MaRDI QIDQ2369870

Jason Swanson

Publication date: 21 June 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507524

zbMATH Keywords

Brownian motionFractional Brownian motionWeak convergenceMedianTightness

Mathematics Subject Classification ID

Gaussian processes (60G15) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Functional limit theorems; invariance principles (60F17)

Related Items (10)

Central limit theorem for a Stratonovich integral with Malliavin calculus ⋮ Couplings and strong approximations to time-dependent empirical processes based on i.i.d. fractional Brownian motions ⋮ Limit Theorems for Quantile and Depth Regions for Stochastic Processes ⋮ A CLT for empirical processes involving time-dependent data ⋮ Convergence rates for rank-based models with applications to portfolio theory ⋮ Central limit theorem for functionals of a generalized self-similar Gaussian process ⋮ Bahadur-Kiefer representations for time dependent quantile processes ⋮ Fluctuations of the empirical quantiles of independent Brownian motions ⋮ Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes ⋮ Empirical quantile central limit theorems for some self-similar processes

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