FROM NONLINEAR FOKKER-PLANCK EQUATIONS TO SOLUTIONS OF DISTRIBUTION DEPENDENT SDE
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.
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1902-1920
1902-1920
Inst Mathematical Statistics