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Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2013, Volume 16, Issue 4, 1350030, 15 pages (Mi idaqp3)  

Application of $p$-adic analysis to time series

A. Yu. Khrennikova, S. V. Kozyrevb, K. Oleschkoc, A. G. Jaramillod, M. de Jesús Correa López

a International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, Växjä, SE-351 95, Sweden
b Department of Mathematical Physics, Steklov Mathematical Institute, RAS, Gubkina Street 8, 119991, Moscow, Russia
c Centro de Geociencias, Universidad Nacional Autónoma de México (UNAM), Campus UNAM Juriquilla, Blvd. Juriquilla 3001, Querétaro, Qro., C.P. 76230, México
d Desarrollo Técnico, TEMPLE, México

Abstract: Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree-like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.

Funding Agency Grant Number
CONACYT - Consejo Nacional de Ciencia y Tecnología 168638
143927
Russian Foundation for Basic Research 11-01-00828-a
Ministry of Education and Science of the Russian Federation NSh-864.2014.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Linnaeus University
Swedish Research Council
This paper was financially supported by the Swedish Scientific Research Council/Swedish Research Link, the project "Non-Archimedean Analysis: From Fundamentals to Applications" and the grant "Math Modeling of Complex Hierarchic Systems," Linnaeus University, and the Projects N 168638 and N 143927 of the SENER-CONACYT-Hidrocarburos Research Program.


DOI: https://doi.org/10.1142/S0219025713500306


Bibliographic databases:

Document Type: Article
MSC: 60G22, 37M10, 26E30
Language: English

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