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- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/BF00047094
- Publisher site
- See Article on Publisher Site
Abstract
The global Markov property (GMP) has been shown in various cases under various conditions by quite different methods. Here we investigate the problem of the GMP (for lattice spin systems) from the nonstandard point of view. By embedding the given system into a hyperfinite system we are able to approximate the conditional expectations that are involved in the formulation of the GMP by internal conditional expectations. This leads to a nonstandard equivalent to the GMP as well as to sufficient nonstandard conditions that are easy to formulate. Finally, we then determine the interrelations between these conditions and some of the standard criteria, thus making their relative position somewhat clearer.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: May 1, 2004