FROM NONLINEAR FOKKER-PLANCK EQUATIONS TO SOLUTIONS OF DISTRIBUTION DEPENDENT SDE

• 成果类型: Article
• 署名作者: Barbu, Viorel; Roeckner, Michael
• 署名单位: Romanian Academy; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1410
• 发表日期: 2020
• 页码: 1902-1920
• 关键词: probabilistic representation; uniqueness; EXISTENCE

摘要

We construct weak solutions to the McKean-Vlasov SDE dX(t) = b(X(t), dL(X(t))/dx (X(t)))dt + sigma(X(t), dL(X(t))/dt (X(t)))dW(t) on R-d for possibly degenerate diffusion matrices sigma with X(0) having a given law, which has a density with respect to Lebesgue measure, dx. Here, L-X(t) denotes the law of X (t). Our approach is to first solve the corresponding nonlinear Fokker-Planck equations and then use the well-known superposition principle to obtain weak solutions of the above SDE.