Lipschitzian complete error calculus and Dirichlet forms
Taking as a starting point Gauss' error calculus (for differentiable functions), the author points out a certain coherence property. In order to extend Gauss' quadratic formula to Lipschitz functions, a reinforced coherence principle is considered and an axiomatic error structure is proposed, in which a Dirichlet form appears [\textit{A. Beurling} and \textit{J. Deny}, Acta Math. 99, 203-224 (1958; Zbl 0089.08106)]. One gets a Lipschitzian complete error calculus, which behaves well by images and by products and also from the point of view of links with experiments; it is suitable, in particular, for infinite-dimensional models met in stochastic analysis. This error calculus is connected with statistics by means of the notion of Fisher information matrix. Three consistent examples for this axiomatic structure are presented. Projective systems of such objects are also considered, in order to catch the delicate question of error permanency, discovered by Poincaré. Finally, a list of conjectures is discussed.
scientific article; zbMATH DE number 1770853
scientific article