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DOI: 10.4230/OASIcs.CCA.2009.2270

Computability of Probability Distributions and Distribution Functions

Authors: Takakazu Mori, Yoshiki Tsujii, and Mariko Yasugi

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

Abstract

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence.

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Takakazu Mori, Yoshiki Tsujii, and Mariko Yasugi. Computability of Probability Distributions and Distribution Functions. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 185-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{mori_et_al:OASIcs.CCA.2009.2270,
  author =	{Mori, Takakazu and Tsujii, Yoshiki and Yasugi, Mariko},
  title =	{{Computability of Probability Distributions and Distribution Functions}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{185--196},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2270},
  URN =		{urn:nbn:de:0030-drops-22704},
  doi =		{10.4230/OASIcs.CCA.2009.2270},
  annote =	{Keywords: Computable probability distribution, computable probability distribution function, effective convergence of probability distributions}
}

Document

DOI: 10.4230/OASIcs.CCA.2009.2275

Random Iteration Algorithm for Graph-Directed Sets

Authors: Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, and Hideki Tsuiki

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

Abstract

A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton's theorem, it is shown that almost all sequences obtained by this algorithm reflect a probability measure which is invariant with respect to the system of contractions with probabilities.

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Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, and Hideki Tsuiki. Random Iteration Algorithm for Graph-Directed Sets. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 245-256, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{tsujii_et_al:OASIcs.CCA.2009.2275,
  author =	{Tsujii, Yoshiki and Mori, Takakazu and Yasugi, Mariko and Tsuiki, Hideki},
  title =	{{Random Iteration Algorithm for Graph-Directed Sets}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{245--256},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2275},
  URN =		{urn:nbn:de:0030-drops-22759},
  doi =		{10.4230/OASIcs.CCA.2009.2275},
  annote =	{Keywords: Random iteration algorithms, graph-directed sets, displaying fractals, invariant probability measures}
}

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Documents authored by Mori, Takakazu

Computability of Probability Distributions and Distribution Functions

Abstract

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Random Iteration Algorithm for Graph-Directed Sets

Abstract

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