Abstract
The existence and non-uniqueness of stationary distributions for distribution dependent stochastic differential equations with regular coefficients and singular coefficients are investigated. The existence of several stationary distributions is referred to as the phase transition. Our criterion on the existence and the non-uniqueness allow the drift to be in the non-gradient case and the noise to be multiplicative and depend on the law of the solution. By using our criterion, McKean-Vlasov stochastic equations in double-wells landscape with the quadratic interaction and the non-quadratic interaction driven by distribution dependent multiplicative noise are investigated.
Funding Statement
Supported by the National Natural Science Foundation of China (Grant No. 11901604, 11771326), and Program for Innovation Research in Central University of Finance and Economics.
Acknowledgments
The author thanks referees for their useful comments.
Citation
Shao-Qin Zhang. "Existence and non-uniqueness of stationary distributions for distribution dependent SDEs." Electron. J. Probab. 28 1 - 34, 2023. https://doi.org/10.1214/23-EJP981
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