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Hilbert's Sixth Problem: Descriptive Statistics as New Foundations for Probability: Lévy Processes

Author

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  • Johnson, Joseph F.

Abstract

Hay esbozos según los cuales las probabilidades se cuentan como la fundación de la teoría matemática de las estadísticas. Mas la significación física de las probabilidades matemáticas son oscuros, muy poco entendidos. Parecíera mejor que las probabilidades físicas se fundaran en las estadísticas descriptivas de datos fisicales. Se trata una teoría que así responde a una cuestiona de Hilbert propuesta en su Problema Número Seis, la axiomatización de la Física. Esta está basada en la auto-correlación de los series temporales. Casi todas de las funciones de auto-correlación de las trayectorías de un sistema dinámico lineal (con un numbero bastante grande de grados de libertad) son todas aproximadamente iguales, no importan las condiciones iniciales, aún si el sistema no sea ergódico, como conjeturó Khintchine en 1943.

Suggested Citation

  • Johnson, Joseph F., 2013. "Hilbert's Sixth Problem: Descriptive Statistics as New Foundations for Probability: Lévy Processes," MPRA Paper 1242, University Library of Munich, Germany, revised 24 May 2014.
    • Handle: RePEc:pra:mprapa:1242
    as

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    File URL: https://mpra.ub.uni-muenchen.de/1242/1/MPRA_paper_1242.pdf
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    References listed on IDEAS

    as
    1. Skyrms, Brian, 1988. "Probability and causation," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 53-68.
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    More about this item

    Keywords

    Time-series; Physical Probability; Lévy Process;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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