Keywords: memory flow, space–time nonlocality, nonlocality parameter, Cantor staircase, fractional (fractal) Brownian motion
@article{TMF_2017_193_1_a7,
author = {N. S. Arkashov and V. A. Seleznev},
title = {Formation of a~relation of nonlocalities in the~anomalous diffusion model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {115--132},
year = {2017},
volume = {193},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a7/}
}
TY - JOUR AU - N. S. Arkashov AU - V. A. Seleznev TI - Formation of a relation of nonlocalities in the anomalous diffusion model JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2017 SP - 115 EP - 132 VL - 193 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a7/ LA - ru ID - TMF_2017_193_1_a7 ER -
N. S. Arkashov; V. A. Seleznev. Formation of a relation of nonlocalities in the anomalous diffusion model. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 1, pp. 115-132. http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a7/
[1] R. Metzler, J. Klafter, “The random walk's guide to anomalous diffusion: a fractional dynamics approach”, Phys. Rep., 339:1 (2000), 1–77 | DOI | MR | Zbl
[2] V. V. Uchaikin, “Avtomodelnaya anomalnaya diffuziya i ustoichivye zakony”, UFN, 173:8 (2003), 847–876 | DOI | DOI
[3] B. B. Mandelbrot, J. W. Van Ness, “Fractional Brownian motions, fractional noises and applications”, SIAM Rev., 10:4 (1968), 422–437 | DOI | MR | Zbl
[4] A. I. Olemskoi, A. Ya. Flat, “Ispolzovanie kontseptsii fraktala v fizike kondensirovannoi sredy”, UFN, 163:12 (1993), 1–50 | DOI | DOI | MR
[5] R. R. Nigmatullin, “Drobnyi integral i ego fizicheskaya interpretatsiya”, TMF, 90:3 (1992), 354–368 | DOI | MR | Zbl
[6] V. P. Budaev, S. P. Savin, L. M. Zelenyi, “Nablyudeniya peremezhaemosti i obobschennogo samopodobiya v turbulentnykh pogranichnykh sloyakh laboratornoi i magnitosfernoi plazmy: na puti k opredeleniyu kolichestvennykh kharakteristik perenosa”, UFN, 189:9 (2011), 905–952 | DOI | DOI
[7] V. P. Budaev, L. N. Khimchenko, “O fraktalnoi strukture osazhdennykh plenok v tokamake”, ZhETF, 131:4 (2007), 711–728 | DOI
[8] A. A. Khamzin, R. R. Nigmatullin, I. I. Popov, “Mikroskopicheskaya model nedebaevskoi dielektricheskoi relaksatsii. Zakon Koula–Koula i ego obobschenie”, TMF, 173:2 (2012), 314–332 | DOI | DOI
[9] I. A. Ibragimov, Yu. V. Linnik, Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965 | MR | MR | Zbl
[10] N. S. Arkashov, I. S. Borisov, “Gaussovskaya approksimatsiya protsessov chastnykh summ skolzyaschikh srednikh”, Sib. matem. zhurn., 45:6 (2004), 1221–1255 | DOI | MR | Zbl
[11] T. Konstantopoulos, A. Sakhanenko, “Convergence and convergence rate to fractional Brownian motion for weighted random sums”, Sib. elektron. matem. izv., 1 (2004), 47–63 | MR | Zbl
[12] G. Edgar, Measure, Topology, and Fractal Geometry, Springer, New York, 2008 | DOI | MR
[13] L. N. Bolshev, N. V. Smirnov, Tablitsy matematicheskoi statistiki, Nauka, M., 1983 | MR
[14] E. Alós, O. Mazet, D. Nualart, “Stochastic calculus with respect to Gaussian processes”, Ann. Probab., 29:2 (2001), 766–801 | DOI | MR | Zbl
[15] E. Feder, Fraktaly, Mir, M., 1991 | DOI | MR | MR | Zbl
[16] M. Lidbetter, G. Lindgren, Kh. Rotsen, Ekstremumy sluchainykh posledovatelnostei i protsessov, Mir, M., 1989 | MR | MR | Zbl | Zbl
[17] E. A. Gorin, B. N. Kukushkin, “Integraly, svyazannye s kantorovoi lestnitsei”, Algebra i analiz, 15:3 (2003), 188–220 | DOI | MR | Zbl
[18] P. Billingsli, Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | DOI | MR | MR | Zbl