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Nonstandard analysis and representation of reality

Claude Lobry 1 Tewfik Sari 1, 2 
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
Abstract : The aim of this paper is to show that the representation with the help of Nonstandard Analysis of a real phenomenon, presenting different observation scales, allows an important simplification of language. Indeed, it is convenient to have available the concept of infinitely small and infinitely large quantities in dealing with the macroscopic effects of microscopic phenomena. This is illustrated on two examples : the representation of two time scales systems and the representation of noise.
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Submitted on : Wednesday, September 4, 2013 - 10:03:25 AM
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Claude Lobry, Tewfik Sari. Nonstandard analysis and representation of reality. International Journal of Control, Taylor & Francis, 2008, 81 (3), pp.519-536. ⟨10.1080/00207170701601728⟩. ⟨hal-00857828⟩



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