Convergence of Riesz space martingales

DOI10.1016/S0019-3577(06)80021-2zbMath1105.47034MaRDI QIDQ2503003

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

Publication date: 13 September 2006

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

stopping timeconditional expectationRiesz space

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Generalizations of martingales (60G48) Stopping times; optimal stopping problems; gambling theory (60G40) Linear operators on ordered spaces (47B60)

Related Items

An Andô-Douglas type theorem in Riesz spaces with a conditional expectation, Ergodic theory and the strong law of large numbers on Riesz spaces, The Itô integral for martingales in vector lattices, Markov processes on 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, The Itô integral and near-martingales in Riesz spaces, Amarts on Riesz spaces, The sup-completion of a Dedekind complete vector lattice, Convergence in Riesz spaces with conditional expectation operators, Mixing inequalities in Riesz spaces, The quadratic variation of continuous time stochastic processes in vector lattices, Jensen's and martingale inequalities in Riesz spaces, The Kolmogorov-Čentsov theorem and Brownian motion in vector lattices, Quadratic variation of martingales in Riesz spaces, Burkholder theorem in Riesz spaces, The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces, Girsanov's theorem in vector lattices, Unbounded order convergence and application to martingales without probability, Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

Cites Work

• Banach lattices
• Characterizations of conditional expectation-type operators
• Conditional expectations on Riesz spaces
• Discrete-time stochastic processes on Riesz spaces.
• Convergence of Martingales with a Directed Index Set
• Stopping Time Techniques for Analysts and Probabilists
• Stopping Times and Directed Processes
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