4 papers
A Note on the instability of equilibria for distribution dependent SDEs
Shao-Qin Zhang
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential eq…
Local convergence near equilibria for distribution dependent SDEs
Shao-Qin Zhang
Owing to exhibiting phase transitions, we investigate the local convergence near a stationary distribution for distribution dependent stochastic differential equations. By lineariz…
A Local Bifurcation Theorem for McKean-Vlasov Diffusions
Shao-Qin Zhang
We establish an existence result of a solution to a class of probability measure-valued equations, whose solutions can be associated with stationary distributions of many McKean-Vl…
A Zvonkin's transformation for stochastic differential equations with singular drift and related applications
Chenggui Yuan, Shao-Qin Zhang
In this paper, by establishing the - estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first or…