From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE
Barbu V, Röckner M (2020)
Annals of Probability 48(4): 1902-1920.
Zeitschriftenaufsatz
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Autor*in
Barbu, Viorel;
Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
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.
Stichworte
Fokker-Planck equation;
Kolmogorov operator;
probability density;
m-accretive operator;
Wiener process
Erscheinungsjahr
2020
Zeitschriftentitel
Annals of Probability
Band
48
Ausgabe
4
Seite(n)
1902-1920
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2945459
Zitieren
Barbu V, Röckner M. From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE. Annals of Probability. 2020;48(4):1902-1920.
Barbu, V., & Röckner, M. (2020). From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE. Annals of Probability, 48(4), 1902-1920. https://doi.org/10.1214/19-AOP1410
Barbu, Viorel, and Röckner, Michael. 2020. “From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE”. Annals of Probability 48 (4): 1902-1920.
Barbu, V., and Röckner, M. (2020). From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE. Annals of Probability 48, 1902-1920.
Barbu, V., & Röckner, M., 2020. From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE. Annals of Probability, 48(4), p 1902-1920.
V. Barbu and M. Röckner, “From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE”, Annals of Probability, vol. 48, 2020, pp. 1902-1920.
Barbu, V., Röckner, M.: From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE. Annals of Probability. 48, 1902-1920 (2020).
Barbu, Viorel, and Röckner, Michael. “From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE”. Annals of Probability 48.4 (2020): 1902-1920.
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