A Note on the instability of equilibria for distribution dependent SDEs
Probability
2025-10-07 v1
Abstract
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a stationary distribution, and links the instability to a spectral property of the generator of the corresponding linearized semigroup to the stochastic equation. Concrete examples, such as the granular media equation with double-wells landscapes, are given to illustrate our main result.
Keywords
Cite
@article{arxiv.2510.04169,
title = {A Note on the instability of equilibria for distribution dependent SDEs},
author = {Shao-Qin Zhang},
journal= {arXiv preprint arXiv:2510.04169},
year = {2025}
}