### Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs

Huang X, Röckner M, Wang F-Y (2019)
Discrete and Continuous Dynamical Systems 39(6): 3017-3035.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Huang, Xing; Röckner, MichaelUniBi; Wang, Feng-Yu
Abstract / Bemerkung
By investigating path-distribution dependent stochastic differential equations, the following type of nonlinear Fokker-Planck equations for probability measures (mu(t)) t >= 0 on the path space l := C([-r(0), 0]; R-d), is analyzed: partial derivative(t)mu(t) = L-t*(,mu t)mu t, t >= 0, where mu(t) is the image of mu(t) under the projection l (sic) xi bar right arrow xi(0) is an element of R-d, and L-t(,mu)(xi) :=1/2 Sigma(d)(i,j=1) aij(t, xi, mu) partial derivative(2)/partial derivative(xi(0)i)partial derivative(xi)(0)(j) + Sigma(d)(i=1) bi(t, xi, mu)partial derivative/partial derivative(xi(0)i), t >= 0, xi is an element of l, mu is an element of P-l. Under reasonable conditions on the coefficients a(ij) and b(i), the existence, uniqueness, Lipschitz continuity in Wasserstein distance, total variational norm and entropy, as well as derivative estimates are derived for the martingale solutions.
Stichworte
Nonlinear PDE for probability measures; path-distribution dependent; SDEs; Wasserstein distance; Harnack inequality; coupling by change of; measure
Erscheinungsjahr
2019
Zeitschriftentitel
Discrete and Continuous Dynamical Systems
Band
39
Ausgabe
6
Seite(n)
3017-3035
ISSN
1078-0947
eISSN
1553-5231
Page URI
https://pub.uni-bielefeld.de/record/2934374

### Zitieren

Huang X, Röckner M, Wang F-Y. Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs. Discrete and Continuous Dynamical Systems. 2019;39(6):3017-3035.
Huang, X., Röckner, M., & Wang, F. - Y. (2019). Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs. Discrete and Continuous Dynamical Systems, 39(6), 3017-3035. doi:10.3934/dcds.2019125
Huang, X., Röckner, M., and Wang, F. - Y. (2019). Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs. Discrete and Continuous Dynamical Systems 39, 3017-3035.
Huang, X., Röckner, M., & Wang, F.-Y., 2019. Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs. Discrete and Continuous Dynamical Systems, 39(6), p 3017-3035.
X. Huang, M. Röckner, and F.-Y. Wang, “Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs”, Discrete and Continuous Dynamical Systems, vol. 39, 2019, pp. 3017-3035.
Huang, X., Röckner, M., Wang, F.-Y.: Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs. Discrete and Continuous Dynamical Systems. 39, 3017-3035 (2019).
Huang, Xing, Röckner, Michael, and Wang, Feng-Yu. “Nonlinear Fokker–Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs”. Discrete and Continuous Dynamical Systems 39.6 (2019): 3017-3035.

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