A Kolmogorov-Chentsov type theorem on general metric spaces with applications to limit theorems for Banach-valued processes

DOI10.1007/s10959-022-01207-8arXiv2107.13837WikidataQ123223125 ScholiaQ123223125MaRDI QIDQ6111876

Mikhail A. Urusov, Volker Krätschmer

Publication date: 4 August 2023

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.13837

zbMATH Keywords

covering numbersuniform tightnessBanach-valued central limit theoremsKolmogorov-Chentsov-type theoremsTalagrand's chaining technique

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Sample path properties (60G17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (1)

Gaussian Whittle-Matérn fields on metric graphs

Cites Work

• Gaussian characterizations of certain Banach spaces
• The law of large numbers and the central limit theorem in Banach spaces
• Weak convergence and empirical processes. With applications to statistics
• A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations
• Wasserstein convergence rates for random bit approximations of continuous Markov processes
• Foundations of Modern Probability
• Upper and Lower Bounds for Stochastic Processes
• A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
• Riemannian geometry and geometric analysis
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