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 semiflow 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.
of a one dimensional dynamical system. We will focus in a semiflow 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.
| Original language | English |
|---|---|
| Journal | Journal of Statistical Physics |
| Volume | 163 |
| Issue number | 1 |
| Pages (from-to) | 113-138 |
| Number of pages | 26 |
| ISSN | 0022-4715 |
| DOIs | |
| Publication status | Published - 2016 |
| MoE publication type | A1 Journal article-refereed |
Fields of Science
- 111 Mathematics
- Perturbed dynamical systems
- 112 Statistics and probability
- Stochastic differential equations
- Total variation distance
- 114 Physical sciences
- Cut-off phenomenon
- Brownian motion