Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

@article{Kuo2007ErgodicTA,
  title={Ergodic theory and the Strong Law of Large Numbers on Riesz spaces},
  author={Wen-Chi Kuo and Coenraad C. A. Labuschagne and Bruce A. Watson},
  journal={Journal of Mathematical Analysis and Applications},
  year={2007},
  volume={325},
  pages={422-437}
}
Discrete stochastic integration in Riesz spaces
In this work we continue the developments of Kuo et al. (Indag Math 15:435–451, 2004; J Math Anal Appl 303:509–521, 2005) with the construction of the martingale transform or discrete stochastic
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We extend the Koopman-von Neumann convergence condition on the Ces\`{a}ro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of
Markov processes on Riesz spaces
Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these
The sup-completion of a Dedekind complete vector lattice
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We study those aspects of continuous stochastic processes in Riesz spaces that enable us to state and prove the Doob–Meyer decomposition theorem for submartingales. We use the concepts developed for
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