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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 477–484
DOI: https://doi.org/10.4213/tmf9253 (Mi tmf9253) 		 
Functional equation for the crossover in the model of one-dimensional Weierstrass random walks

Yu. G. Rudoia, O. A. Kotel'nikovab

a Peoples' Friendship University of Russia, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf9253
Abstract: We consider the problem of one-dimensional symmetric diffusion in the framework of Markov random walks of the Weierstrass type using two-parameter scaling for the transition probability. We construct a solution for the characteristic Lyapunov function as a sum of regular (homogeneous) and singular (nonhomogeneous) solutions and find the conditions for the crossover from normal to anomalous diffusion.
Keywords: normal diffusion, anomalous diffusion, Markov process, fractal dimension, functional pressure, Weierstrass function.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
This research was supported by the Ministry of Education and Science of the Russian Federation, Russian Academic Excellence Program for the Peoples' Friendship University of Russia, 2016-2020.
Received: 18.07.2016
Revised: 01.08.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1818–1823
DOI: https://doi.org/10.1134/S0040577916120138
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. G. Rudoi, O. A. Kotel'nikova, “Functional equation for the crossover in the model of one-dimensional Weierstrass random walks”, TMF, 189:3 (2016), 477–484; Theoret. and Math. Phys., 189:3 (2016), 1818–1823
Citation in format AMSBIB
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