Computability of Probability Distributions and Characteristic Functions
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.
Férée, Hugo; Ziegler, Martin, 2016, On The Computational Complexity Of Positive Linear Functionals On $$\Mathcal{C}[0;1]$$, Mathematical Aspects Of Computer And Information Sciences - Lecture Notes In Computer Science, pp. 489-504, 10.1007/978-3-319-32859-1_42.