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Chorro, Christophe

On an extension of the Hilbertian central limit theorem to Dirichlet forms. (English) Zbl 1159.31003

Osaka J. Math. 45, No. 2, 457-470 (2008).
N. Bouleau [J. Math. Pures Appl., IX. Sér. 80, No. 9, 961–976 (2001; Zbl 1031.31005)] introduced a new tool, based on the language of Dirichlet forms, in order to study the propagation of errors and reinforce the historical approach of Gauss. In the same way that the practical use of the normal distribution in statistics may be explained by the central limit theorem, the aim of this paper is to underline the importance of a family of error structures by asymptotic arguments.
Reviewer: Liliana Popa (Iaşi)

MSC:

31C25 Dirichlet forms
47B25 Linear symmetric and selfadjoint operators (unbounded)
49Q12 Sensitivity analysis for optimization problems on manifolds
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60F05 Central limit and other weak theorems

Keywords:

propagation of errors, Dirichlet forms

Citations:

Zbl 1031.31005
Cite Review PDF
Full Text: Euclid

References:

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