Bismut formula for Lions derivative of distribution dependent SDEs and applications

Panpan Ren; Feng-Yu Wang

doi:10.1016/j.jde.2019.05.016

Author(s)

Panpan Ren
Feng-Yu Wang

Detail(s)

Original language	English
Pages (from-to)	4745-4777
Journal / Publication	Journal of Differential Equations
Volume	267
Issue number	8
Online published	15 May 2019
Publication status	Published - 5 Oct 2019
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1016/j.jde.2019.05.016 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85065560281&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(3bb9a0ad-92e9-400d-a07f-b4f7dc5f91bb).html

Abstract

By using Malliavin calculus, Bismut type formulas are established for the Lions derivative of P_tf (μ): = Ef (X_t^μ), where t > 0, f is a bounded measurable function, and X_t^μ solves a distribution dependent SDE with initial distribution μ. As applications, explicit estimates are derived for the Lions derivative and the total variational distance between distributions of solutions with different initial data. Both degenerate and non-degenerate situations are considered. Due to the lack of the semigroup property and the invalidity of the formula P_tf (μ) = ∫P_tf (x) μ (dx), essential difficulties are overcome in the study.

© 2019 Elsevier Inc. All rights reserved.

Research Area(s)

Bismut formula, Distribution dependent SDEs, L-derivative, Wasserstein distance

Citation Format(s)

[ RIS ] [ BibTeX ]

Bismut formula for Lions derivative of distribution dependent SDEs and applications. / Ren, Panpan; Wang, Feng-Yu.
In: Journal of Differential Equations, Vol. 267, No. 8, 05.10.2019, p. 4745-4777.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Ren, P & Wang, F-Y 2019, 'Bismut formula for Lions derivative of distribution dependent SDEs and applications', Journal of Differential Equations, vol. 267, no. 8, pp. 4745-4777. https://doi.org/10.1016/j.jde.2019.05.016

Ren, P., & Wang, F-Y. (2019). Bismut formula for Lions derivative of distribution dependent SDEs and applications. Journal of Differential Equations, 267(8), 4745-4777. https://doi.org/10.1016/j.jde.2019.05.016

Ren P, Wang F-Y. Bismut formula for Lions derivative of distribution dependent SDEs and applications. Journal of Differential Equations. 2019 Oct 5;267(8):4745-4777. Epub 2019 May 15. doi: 10.1016/j.jde.2019.05.016

Ren, Panpan ; Wang, Feng-Yu. / Bismut formula for Lions derivative of distribution dependent SDEs and applications. In: Journal of Differential Equations. 2019 ; Vol. 267, No. 8. pp. 4745-4777.