An Andô-Douglas type theorem in Riesz spaces with a conditional expectation

DOI10.1007/s11117-008-2239-2zbMath1186.47038OpenAlexW2030671173MaRDI QIDQ839541

Bruce Alastair Watson

Publication date: 2 September 2009

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-008-2239-2

zbMATH Keywords

Radon-Nikodým theoremRiesz spacesHahn-Jordan decompositionAndô-Douglas theorem

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 (21)

Maximal probability inequalities in vector lattices ⋮ Near-epoch dependence in Riesz spaces ⋮ 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 ⋮ Chernoff’s inequality in Riesz spaces ⋮ Doob's optional sampling theorem in Riesz spaces ⋮ Ergodicity in Riesz Spaces ⋮ Mixing inequalities in Riesz spaces ⋮ Bernoulli Processes in Riesz Spaces ⋮ The quadratic variation of continuous time stochastic processes in vector lattices ⋮ Stopped processes and Doob's optional sampling theorem ⋮ 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 ⋮ Andô-Douglas type characterization of optional projections and predictable projections ⋮ On the decompositions of \(T\)-quasi-martingales on 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

• Representations of positive projections. I
• Characterizations of conditional expectation-type operators
• An elementary proof of Douglas' theorem on contractive projections on \(L_ 1\)-spaces
• Conditional expectations on Riesz spaces
• The range of a contractive projection on an L\(_p\)-space
• Discrete-time stochastic processes on Riesz spaces.
• Convergence of Riesz space martingales
• Contractive projections on an \(L_ 1\) space
• Stopping Time Techniques for Analysts and Probabilists
• Stopping Times and Directed Processes
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