Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures

[1]  T. Zhukovskaya,et al.  Functional Inequalities , 2021, Inequalities in Analysis and Probability.

[2]  A. Veretennikov,et al.  Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations , 2016 .

[3]  Convergence to Equilibrium in Fokker–Planck Equations , 2018, Journal of Dynamics and Differential Equations.

[4]  A. I. Kirillov,et al.  Distances between Stationary Distributions of Diffusions and Solvability of Nonlinear Fokker--Planck--Kolmogorov Equations , 2018 .

[5]  A. Eberle,et al.  Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes , 2016, Transactions of the American Mathematical Society.

[6]  S. V. Shaposhnikov Nonlinear Fokker–Planck–Kolmogorov Equations for Measures , 2016 .

[7]  Vladimir I. Bogachev,et al.  Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations , 2016 .

[8]  Feng-Yu Wang Distribution-Dependent SDEs for Landau Type Equations , 2016, 1606.05843.

[9]  Vladimir I. Bogachev,et al.  Fokker-planck-kolmogorov Equations , 2015 .

[10]  O. Manita Estimates for the Kantorovich distances between solutions to the nonlinear Fokker-Planck-Kolmogorov equation with monotone drift , 2015 .

[11]  The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker-Planck-Kolmogorov equations , 2014 .

[12]  Oxana A. Manita,et al.  On uniqueness of solutions to nonlinear Fokker-Planck-Kolmogorov equations , 2014, 1407.8047.

[13]  Jian Wang,et al.  Exponential convergence in Lp ‐Wasserstein distance for diffusion processes without uniformly dissipative drift , 2014, 1407.1986.

[14]  Patrick Cattiaux,et al.  Long time behavior of Markov processes , 2014 .

[15]  Oleg Butkovsky,et al.  On Ergodic Properties of Nonlinear Markov Chains and Stochastic McKean--Vlasov Equations , 2013, 1311.6367.

[16]  A. Eberle Couplings, distances and contractivity for diffusion processes revisited , 2013 .

[17]  S. V. Shaposhnikov,et al.  Nonlinear parabolic equations for measures , 2012 .

[18]  S. Glotzer,et al.  Time-course gait analysis of hemiparkinsonian rats following 6-hydroxydopamine lesion , 2004, Behavioural Brain Research.

[19]  Nonlinear elliptic equations for measures , 2011 .

[20]  J. Carrillo,et al.  Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations , 2011 .

[21]  Jonathan C. Mattingly,et al.  Yet Another Look at Harris’ Ergodic Theorem for Markov Chains , 2008, 0810.2777.

[22]  S. Varadhan,et al.  Large deviations , 2019, Graduate Studies in Mathematics.

[23]  Samuel Herrmann Julian Tugaut Non-uniqueness of stationary measures for self-stabilizing processes , 2009, 0903.2460.

[24]  Ivan Gentil,et al.  Phi-entropy inequalities for diffusion semigroups , 2008, 0812.0800.

[25]  Qiangchang Ju,et al.  Large-time behavior of non-symmetric Fokker-Planck type equations , 2008 .

[26]  D. Bakry,et al.  Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré , 2007, math/0703355.

[27]  C. Villani,et al.  Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media , 2006 .

[28]  A. Veretennikov,et al.  On Ergodic Measures for McKean-Vlasov Stochastic Equations , 2006 .

[29]  T. D. Frank,et al.  Nonlinear Fokker-Planck Equations , 2005 .

[30]  王 风雨 Functional inequalities, Markov semigroups and spectral theory , 2005 .

[31]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[32]  T. Frank Nonlinear Fokker-Planck Equations: Fundamentals and Applications , 2004 .

[33]  M. Röckner,et al.  Harnack and functional inequalities for generalized Mehler semigroups , 2003 .

[34]  Giuseppe Toscani,et al.  ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS , 2001 .

[35]  S. Benachour,et al.  Nonlinear self-stabilizing processes – II: Convergence to invariant probability , 1998 .

[36]  D. Talay,et al.  Nonlinear self-stabilizing processes – I Existence, invariant probability, propagation of chaos , 1998 .

[37]  S. Meyn,et al.  Exponential and Uniform Ergodicity of Markov Processes , 1995 .

[38]  N. Ahmed,et al.  On invariant measures of nonlinear Markov processes , 1993 .

[39]  Jürgen Gärtner,et al.  Large Deviations, Free Energy Functional and Quasi-Potential for a Mean Field Model of Interacting Diffusions , 1989 .

[40]  Mu-Fa Chen,et al.  Coupling Methods for Multidimensional Diffusion Processes , 1989 .

[41]  田村 要造 Free energy and the convergence of distributions of diffusion processes of McKean type = 自由エネルギーとマッキーン型拡散過程の分布の収束 , 1987 .

[42]  Tadahisa Funaki,et al.  A certain class of diffusion processes associated with nonlinear parabolic equations , 1984 .

[43]  Y. Tamura On asymptotic behaviors of the solution of a nonlinear diffusion equation , 1984 .

[44]  M. Hp A class of markov processes associated with nonlinear parabolic equations. , 1966 .

[45]  M. Kac Foundations of Kinetic Theory , 1956 .