Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting

Pece Trajanovski, Petar Jolakoski, Ljupco Kocarev and Trifce Sandev ()
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Pece Trajanovski: Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
Petar Jolakoski: Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
Ljupco Kocarev: Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
Trifce Sandev: Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia

Mathematics, 2023, vol. 11, issue 16, 1-28

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.

Keywords: Ornstein–Uhlenbeck process; comb structure; stochastic resetting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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