On the functional central limit theorem for martingales

DOI10.1007/BF00537263zbMath0336.60047MaRDI QIDQ4104669

Holger Rootzén

Publication date: 1977

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Mathematics Subject Classification ID

Convergence of probability measures (60B10)

Related Items (15)

On the martingale central limit theorem for strictly stationary sequences ⋮ Unnamed Item ⋮ Relative stability in strictly stationary random sequences ⋮ Central limit theorems and diffusion approximations for multiscale Markov chain models ⋮ Diffusion approximation for an overloaded \(X\) model via a stochastic averaging principle ⋮ A note on convergence to mixtures of normal distributions ⋮ Weak convergence of semimartingales ⋮ Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems ⋮ Remarks on the functional central limit theorem for martingales ⋮ On the functional central limit theorem for martingales, II ⋮ On weak convergence to Brownian motion ⋮ Invariance principles for stochastic area and related stochastic integrals ⋮ On a problem of necessary and sufficient conditions in the functional central limit theorem for local martingales ⋮ Necessary and sufficient conditions for the convergence of semimartingales to processes with conditionally independent increments ⋮ Martingale difference arrays and stochastic integrals

Cites Work

• Distribution function inequalities for martingales
• Dependent central limit theorems and invariance principles
• The Lindeberg-Levy Theorem for Martingales
• Martingale Central Limit Theorems
• An Invariance Principle for Martingales
• Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach
• A Central Limit Theorem for a Class of Dependent Random Variables
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