Geodesic
On upper functions for anomalous diffusions governed by time-varying Ornstein--Uhlenbeck process
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 258-282

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We obtain upper functions that serve as almost sure asymptotic upper bounds for a displacement process given by an integrated time-varying Ornstein–Uhlenbeck process. The form of upper functions depends on the characteristics (the stability rate and the diffusion coefficient) of a stochastic linear differential equation. We introduce the notion of anomalous diffusion related to behavior of upper functions and compare the results of diffusion classification (normal diffusion, subdiffusion, and superdiffusion) with those obtained on the basis of mean square displacements.
Keywords: time-varying Ornstein–Uhlenbeck process, upper function, the law of the iterated logarithm.
Mots-clés : anomalous diffusion 
@article{TVP_2019_64_2_a2,
     author = {E. S. Palamarchuk},
     title = {On upper functions for anomalous diffusions governed by time-varying {Ornstein--Uhlenbeck} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {258--282},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_2_a2/}
}
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E. S. Palamarchuk. On upper functions for anomalous diffusions governed by time-varying Ornstein--Uhlenbeck process. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 258-282. http://geodesic.mathdoc.fr/item/TVP_2019_64_2_a2/