Itô's rule and Lévy's theorem in vector lattices

DOI10.1016/j.jmaa.2017.06.011zbMath1377.60064OpenAlexW2621491156MaRDI QIDQ2014075

Coenraad C. A. Labuschagne, Jacobus J. Grobler

Publication date: 10 August 2017

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.2017.06.011

zbMATH Keywords

Brownian motionLévy's theoremItô rule

Mathematics Subject Classification ID

Sample path properties (60G17) Stochastic integrals (60H05) Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items (2)

Maximal probability inequalities in vector lattices ⋮ Girsanov's theorem in vector lattices

Cites Work

• Doob's optional sampling theorem in Riesz spaces
• The Itô integral for Brownian motion in vector lattices. I
• The Itô integral for Brownian motion in vector lattices. II
• The quadratic variation of continuous time stochastic processes in vector lattices
• Continuous stochastic processes in Riesz spaces: The Doob-Meyer decomposition
• Discrete stochastic integration in Riesz spaces
• An Andô-Douglas type theorem in Riesz spaces with a conditional expectation
• Martingales in Banach lattices
• A description of norm-convergent martingales on vector-valued \(L^p\)-spaces
• Ergodic theory and the strong law of large numbers on Riesz spaces
• Extension of positive operators and Korovkin theorems
• Continuity, integration and Fourier theory
• Banach lattices
• Conditional expectations on Riesz spaces
• Discrete-time stochastic processes on Riesz spaces.
• Markov processes on Riesz spaces
• 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
• Uo-convergence and its applications to Cesàro means in Banach lattices
• The Itô integral for martingales in vector lattices
• Convergent martingales of operators and the Radon Nikodým property in Banach spaces
• ON THE FUNCTIONAL CALCULUS IN ARCHIMEDEAN RIESZ SPACES WITH APPLICATIONS TO APPROXIMATION THEOREMS
• A Martingale Convergence Theorem in Vector Lattices
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