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arXiv · 2510.04169

A Note on the instability of equilibria for distribution dependent SDEs

Shao-Qin Zhang
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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.

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Shao-Qin Zhang. 2025-10-05. A Note on the instability of equilibria for distribution dependent SDEs. https://arxiv.org/abs/2510.04169

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