A Note on the instability of equilibria for distribution dependent SDEs

2025/10/05 by Zhang, Shao-Qin
#60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.04169

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.

Citations

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Related

• Local convergence near equilibria for distribution dependent SDEs
• Existence and non-uniqueness of stationary distributions for distribution dependent SDEs
• Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs
• Distribution-Dependent SDEs for Landau Type Equations
• Doubly nonlinear stochastic evolution equations II