Limit theorems for additive functionals of a Markov chain

DOI10.1214/09-AAP610zbMath1232.60018arXiv0809.0177OpenAlexW3103197793MaRDI QIDQ1049564

Tomasz Komorowski, Milton D. Jara, Stefano Olla

Publication date: 13 January 2010

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.0177

zbMATH Keywords

stable laws limit theorems anomalous heat transport fractional heat equation linear Boltzmann equation self-similar Lévy processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Functional limit theorems; invariance principles (60F17)

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Cites Work