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

Johnson, Joseph F. (2013): Hilbert's Sixth Problem: Descriptive Statistics as New Foundations for Probability: Lévy Processes. Published in: Revista Investigación Operacional , Vol. 35, No. 2 (April 2014): pp. 173-179.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Time-series; Physical Probability; Lévy Process
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools

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