Search results for "Representation theorem"

showing 2 items of 32 documents

Fractional Brownian motion and Martingale-differences

2004

Abstract We generalize a result of Sottinen (Finance Stochastics 5 (2001) 343) by proving an approximation theorem for the fractional Brownian motion, with H> 1 2 , using martingale-differences.

Statistics and ProbabilityGeometric Brownian motionFractional Brownian motionMathematics::ProbabilityDiffusion processReflected Brownian motionMathematical analysisBrownian excursionStatistics Probability and UncertaintyHeavy traffic approximationMartingale (probability theory)Martingale representation theoremMathematicsStatistics & Probability Letters
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Finitary formal topologies and Stone’s representation theorem

2008

AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.

Stone's representationGeneral Computer ScienceRelation (database)Representation theoremFormal topologyformal topology; positivity; Stone's representation; constructive methodsPositivityBasis (universal algebra)Topological spaceStone’s representationMathematical proofConstructiveTheoretical Computer ScienceConstructive methodsAlgebraDistributive propertyFinitaryComputer Science(all)MathematicsTheoretical Computer Science
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