Well-posedness of distribution dependent SDEs with singular drifts
Röckner M, Zhang X (2021)
Bernoulli 27(2): 1131-1158.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Abstract / Bemerkung
Consider the following distribution dependent SDE: dX(t) = sigma(t)(X-t, mu X-t) dW(t) + b(t)(X-t, mu X-t) dt, where mu X-t stands for the distribution of X-t. In this paper for non-degenerate sigma, we show the strong well-posedness of the above SDE under some integrability assumptions in the spatial variable and Lipschitz continuity in mu about b and sigma. In particular, we extend the results of Krylov-Rockner (Probab. Theory Related Fields 131 (2005) 154-196) to the distribution dependent case.
Stichworte
Distribution dependent SDEs;
Zvonkin's transformation;
singular drifts;
superposition principle;
McKean-Vlasov system
Erscheinungsjahr
2021
Zeitschriftentitel
Bernoulli
Band
27
Ausgabe
2
Seite(n)
1131-1158
ISSN
1350-7265
eISSN
1573-9759
Page URI
https://pub.uni-bielefeld.de/record/2954224
Zitieren
Röckner M, Zhang X. Well-posedness of distribution dependent SDEs with singular drifts. Bernoulli . 2021;27(2):1131-1158.
Röckner, M., & Zhang, X. (2021). Well-posedness of distribution dependent SDEs with singular drifts. Bernoulli , 27(2), 1131-1158. https://doi.org/10.3150/20-BEJ1268
Röckner, Michael, and Zhang, Xicheng. 2021. “Well-posedness of distribution dependent SDEs with singular drifts”. Bernoulli 27 (2): 1131-1158.
Röckner, M., and Zhang, X. (2021). Well-posedness of distribution dependent SDEs with singular drifts. Bernoulli 27, 1131-1158.
Röckner, M., & Zhang, X., 2021. Well-posedness of distribution dependent SDEs with singular drifts. Bernoulli , 27(2), p 1131-1158.
M. Röckner and X. Zhang, “Well-posedness of distribution dependent SDEs with singular drifts”, Bernoulli , vol. 27, 2021, pp. 1131-1158.
Röckner, M., Zhang, X.: Well-posedness of distribution dependent SDEs with singular drifts. Bernoulli . 27, 1131-1158 (2021).
Röckner, Michael, and Zhang, Xicheng. “Well-posedness of distribution dependent SDEs with singular drifts”. Bernoulli 27.2 (2021): 1131-1158.
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