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Title: Discretisations of higher order and the theorems of
Authors: Van den Berg, Imme
Editors: Cutland, Nigel
Keywords: Difference quotients
Chain rule
Fa`a di Bruno Theorem
nonstandard analysis
Issue Date: 2013
Publisher: Association of Symbolic Logic
Citation: Imme van den Berg, Discretisations of higher order and the theorems of Fa`a di Bruno and DeMoivreLaplace, Journal of Logic & Analysis 5:6 (2013) 1–35 ISSN 17599008
Abstract: We study discrete functions on equidistant and nonequidistant infinitesimal grids. We consider their difference quotients of higher order and give conditions for their nearequality to the corresponding derivatives. Important tools are nonstandard notions of regularity of higher order, and the formula of Fa`a di Bruno for higher order derivatives and a iscrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivreLaplace Theorem to higher order: nth order difference quotients of the binomial probability distribution tend to the corresponding nth order partial differential quotients of the Gaussian distribution.
ISSN: 1759-9008
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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