Geodesic
Functional equation for the~crossover in the~model of one-dimensional Weierstrass random walks
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 477-484

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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.
Mots-clés : normal diffusion, anomalous diffusion, fractal dimension
Keywords: Markov process, functional pressure, Weierstrass function. 
@article{TMF_2016_189_3_a12,
     author = {Yu. G. Rudoi and O. A. Kotel'nikova},
     title = {Functional equation for the~crossover in the~model of one-dimensional {Weierstrass} random walks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {477--484},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a12/}
}
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Yu. G. Rudoi; O. A. Kotel'nikova. Functional equation for the~crossover in the~model of one-dimensional Weierstrass random walks. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 477-484. http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a12/