Abrupt convergence for stochastic small perturbations of one dimensional dynamical systems
Probability
2023-05-08 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white noise of small variance. Under suitable hypothesis on the potential we will prove that the family of perturbed stochastic differential equations present a profile cut-off phenomenon with respect to the total variation distance. We also prove a local cut-off phenomenon in a neighborhood of the local minima (metastable states) of multi-well potential.
Keywords
Cite
@article{arxiv.1511.00003,
title = {Abrupt convergence for stochastic small perturbations of one dimensional dynamical systems},
author = {Gerardo Barrera and Milton Jara},
journal= {arXiv preprint arXiv:1511.00003},
year = {2023}
}
Comments
28 pages. arXiv admin note: substantial text overlap with arXiv:1510.09207; text overlap with arXiv:math/0601771 by other authors