Computability of Probability Distributions and Characteristic FunctionsArticle
Authors: Takakazu Mori ; Yoshiki Tsujii ; Mariko Yasugi
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Takakazu Mori;Yoshiki Tsujii;Mariko Yasugi
As a part of our works on effective properties of probability distributions,
we deal with the corresponding characteristic functions. A sequence of
probability distributions is computable if and only if the corresponding
sequence of characteristic functions is computable. As for the onvergence
problem, the effectivized Glivenko's theorem holds. Effectivizations of
Bochner's theorem and de Moivre-Laplace central limit theorem are also proved.
Hugo Férée;Martin Ziegler, Lecture notes in computer science, On the Computational Complexity of Positive Linear Functionals on $$\mathcal{C}[0;1]$$, pp. 489-504, 2016, 10.1007/978-3-319-32859-1_42.