Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting
Abstract
We analyse two-dimensional isotropic heterogeneous diffusion with a radially decaying diffusion coefficient D(ρ) = D 0 /ρ 2 , subject to Poissonian stochastic resetting to the origin. Since multiplicative noise makes the process interpretation-dependent, we treat the Itô, Stratonovich, and Hänggi-Klimontovich prescriptions within a single approach. For each, we obtain the exact probability density function, the non-equilibrium stationary state induced by resetting, the mean squared displacement, and the first-passage properties. The non-equilibrium stationary state is governed by modified Bessel functions and departs from the Laplace form found for homogeneous diffusion under resetting, while the mean squared displacement saturates at long times as ⟨ρ 2 ⟩ ∼ r-1/2 , r being the resetting rate. The mean firstpassage time to an absorbing boundary exhibits an optimal resetting rate at which it is minimized. In addition, we incorporate memory effects through a subordination (continuous-time random walk) approach with a power-law kernel, deriving the fractional Fokker-Planck equation together with the non-equilibrium stationary state, the mean squared displacement expressed via the three-parameter Mittag-Leffler function, and the first-passage statistics; the optimal resetting rate increases as the memory exponent decreases.
Related
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BibTeX
@misc{sandev2026heterogeneous,
title = {{Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting}},
author = {Trifce Sandev and Sébastien Fumeron and Malte Henkel and Ervin K Lenzi},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24427},
eprint = {2609.24427},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05757081v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting
AU - Trifce Sandev
AU - Sébastien Fumeron
AU - Malte Henkel
AU - Ervin K Lenzi
PY - 2026
DA - 2026/09/21
PB - HAL
DO - 10.48550/arxiv.2609.24427
UR - https://hal.science/hal-05757081v1
AB - We analyse two-dimensional isotropic heterogeneous diffusion with a radially decaying diffusion coefficient D(ρ) = D 0 /ρ 2 , subject to Poissonian stochastic resetting to the origin. Since multiplicative noise makes the process interpretation-dependent, we treat the Itô, Stratonovich, and Hänggi-Klimontovich prescriptions within a single approach. For each, we obtain the exact probability density function, the non-equilibrium stationary state induced by resetting, the mean squared displacement, and the first-passage properties. The non-equilibrium stationary state is governed by modified Bessel functions and departs from the Laplace form found for homogeneous diffusion under resetting, while the mean squared displacement saturates at long times as ⟨ρ 2 ⟩ ∼ r-1/2 , r being the resetting rate. The mean firstpassage time to an absorbing boundary exhibits an optimal resetting rate at which it is minimized. In addition, we incorporate memory effects through a subordination (continuous-time random walk) approach with a power-law kernel, deriving the fractional Fokker-Planck equation together with the non-equilibrium stationary state, the mean squared displacement expressed via the three-parameter Mittag-Leffler function, and the first-passage statistics; the optimal resetting rate increases as the memory exponent decreases.
ER -