On the rate of convergence in the invariance principle for real-valued functions of Doeblin processes

DOI10.1016/0047-259X(84)90068-XzbMath0548.60032MaRDI QIDQ799299

Erich Haeusler

Publication date: 1984

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

rate of convergencefunctional central limit theoremDoeblin's conditionnon-uniform Berry-Esseen estimateProkhorov's metric

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Functional limit theorems; invariance principles (60F17)

Related Items (1)

Diffusive limits of Lipschitz functionals of Poisson measures

Cites Work

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• Upper and lower functions for martingales and mixing processes
• Some probabilistic inequalities for martingales
• The Invariance Principle for Dependent Random Variables
• An exact rate of convergence in the functional central limit theorem for special martingale difference arrays
• On the Rate of Convergence for the Invariance Principle
• A uniform rate of convergence for the maximum absolute value of partial sums in probability
• Rates of Convergence for Some Functionals in Probability
• Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach

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