DISTANCES BETWEEN STATIONARY DISTRIBUTIONS OF DIFFUSIONS AND SOLVABILITY OF NONLINEAR FOKKER-PLANCK-KOLMOGOROV EQUATIONS

被引：6

作者：

Bogachev, V. I. ^{[1
,2
,3
]}

Kirillov, A. I. ^{[4
]}

Shaposhnikov, S. V. ^{[1
,2
,3
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia

[2] St Tikhons Orthodox Univ, Moscow, Russia

[3] Natl Res Univ, Higher Sch Econ, Moscow, Russia

[4] Russian Fdn Basic Res, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2018年 / 62卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

stationary Fokker-Planck-Kolmogorov equation; total variation distance; Kantorovich metric; Prohorov metric; nonlinear Fokker-Planck-Kolmogorov equation; ELLIPTIC-EQUATIONS; INVARIANT-MEASURES; TRANSITION-PROBABILITIES; KANTOROVICH; REGULARITY; DENSITIES;

D O I：

10.1137/S0040585X97T988460

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is concerned with investigation of stationary distributions of diffusion processes. We obtain estimates for the Kantorovich, Prohorov, and total variation distances between stationary distributions of diffusions with different diffusion matrices and different drift coefficients. Applications are given to nonlinear stationary Fokker-Planck-Kolmogorov equations, for which new conditions for the existence and uniqueness of probability solutions are found; moreover, these conditions are optimal in a sense.

引用

页码：12 / 34

页数：23

共 50 条

[1] The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker-Planck-Kolmogorov equations
Bogachev, V. I.
Kirillov, A. I.
Shaposhnikov, S. V.
MATHEMATICAL NOTES, 2014, 96 (5-6) : 855 - 863
[2] The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker-Planck-Kolmogorov equations
V. I. Bogachev
A. I. Kirillov
S. V. Shaposhnikov
Mathematical Notes, 2014, 96 : 855 - 863
[3] Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
Bogachev, V. I.
Roeckner, M.
Shaposhnikov, S. V.
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (05) : 1262 - 1300
[4] Stationary Fokker-Planck-Kolmogorov Equations
Bogachev, Vladimir, I
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RELATED FIELDS: IN HONOR OF MICHAEL ROCKNER, SPDERF, 2018, 229 : 3 - 24
[5] Convergence to Stationary Measures in Nonlinear Fokker-Planck-Kolmogorov Equations
Bogachev, V. I.
Roeckner, M.
Shaposhnikov, S. V.
DOKLADY MATHEMATICS, 2018, 98 (02) : 452 - 457
[6] Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations
V. Ya. Fainberg
Theoretical and Mathematical Physics, 2006, 149 : 1710 - 1725
[7] Nonlinear Fokker-Planck-Kolmogorov Equations for Measures
Shaposhnikov, Stanislav, V
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RELATED FIELDS: IN HONOR OF MICHAEL ROCKNER, SPDERF, 2018, 229 : 367 - 379
[8] Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations
Fainberg, V. Ya.
THEORETICAL AND MATHEMATICAL PHYSICS, 2006, 149 (03) : 1710 - 1725
[9] Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures
Bogachev, Vladimir, I
Roeckner, Michael
Shaposhnikov, Stanislav, V
JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (12) : 3681 - 3713
[10] Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations
Rehmeier, Marco
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 328 : 105 - 132

← 1 2 3 4 5 →