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- Title
Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting.
- Authors
Trajanovski, Pece; Jolakoski, Petar; Kocarev, Ljupco; Sandev, Trifce
- Abstract
The Ornstein–Uhlenbeck (O-U) process with resetting is considered as the anomalous transport taking place on a three-dimensional comb. The three-dimensional comb is a comb inside a comb structure, consisting of backbones and fingers in the following geometrical correspondence x–backbone →y–fingers–backbone →z–fingers. Realisation of the O-U process on the three-dimensional comb leads to anomalous (non-Markovian) diffusion. This specific anomalous transport in the presence of resets results in non-equilibrium stationary states. Explicit analytical expressions for the mean values and the mean squared displacements along all three directions of the comb are obtained and verified numerically. The marginal probability density functions for each direction are obtained numerically by Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry.
- Subjects
ORNSTEIN-Uhlenbeck process; MONTE Carlo method; PROBABILITY density function; LANGEVIN equations
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 16, p3576
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11163576