Ergodic theory and the strong law of large numbers on Riesz spaces

DOI10.1016/j.jmaa.2006.01.056zbMath1114.46015OpenAlexW1974350226MaRDI QIDQ854059

Wen-Chi Kuo, Coenraad C. A. Labuschagne, Bruce Alastair Watson

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.01.056

zbMATH Keywords

projectionslaw of large numbersconditional expectationergodic theoremRiesz spacezero-one law

Mathematics Subject Classification ID

Strong limit theorems (60F15) Banach lattices (46B42) Positive linear operators and order-bounded operators (47B65) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (18)

Maximal probability inequalities in vector lattices ⋮ Limit laws for martingales in vector lattices ⋮ The Itô integral for martingales in vector lattices ⋮ Markov processes on Riesz spaces ⋮ The Kac formula and Poincaré recurrence theorem in Riesz spaces ⋮ Continuous stochastic processes in Riesz spaces: The Doob-Meyer decomposition ⋮ Discrete stochastic integration in Riesz spaces ⋮ Doob's optional sampling theorem in Riesz spaces ⋮ On (in)dependence measures in Riesz spaces ⋮ Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz spaces ⋮ The sup-completion of a Dedekind complete vector lattice ⋮ Ergodicity in Riesz Spaces ⋮ Jensen's and martingale inequalities in Riesz spaces ⋮ The Kolmogorov-Čentsov theorem and Brownian motion in vector lattices ⋮ Itô's rule and Lévy's theorem in vector lattices ⋮ The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces ⋮ Girsanov's theorem in vector lattices ⋮ A Koopman-von Neumann type theorem on the convergence of Cesàro means in Riesz spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Banach lattices
• Characterizations of conditional expectation-type operators
• Conditional expectations on Riesz spaces
• Discrete-time stochastic processes on Riesz spaces.
• Measures and probabilities
• Convergence of Riesz space martingales
• Ergodic theorem without invariant measure
• Weak Laws of Large Numbers in Some Non-Commutative Spaces
• Birkhoff's ergodic theorem and the maximal ergodic theorem

This page was built for publication: Ergodic theory and the strong law of large numbers on Riesz spaces