Transportation cost inequality for backward stochastic differential equations

被引：3

作者：

Bahlali, Khaled ^{[1
]}

Boufoussi, Brahim ^{[2
]}

Mouchtabih, Soufiane ^{[1
,2
]}

机构：

[1] Univ Toulon & Var, IMATH, EA 2134, F-83957 La Garde, France

[2] Cadi Ayyad Univ, Fac Sci Semlalia, Dept Math, Marrakech 2390, Morocco

来源：

STATISTICS & PROBABILITY LETTERS | 2019年 / 155卷

关键词：

Backward stochastic differential equations; Concentration of measure; Transportation-information inequality; Girsanov transformation;

D O I：

10.1016/j.spl.2019.108586

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：

We prove that probability laws of a backward stochastic differential equation, satisfy a quadratic transportation cost inequality under the uniform metric. That is, a comparison of the Wasserstein distance from the law of the solution of the equation to any other absolutely continuous measure with finite relative entropy. From this we derive concentration properties of Lipschitz functions of the solution. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：7

共 13 条

[1] Hypercontractivity of Hamilton-Jacobi equations [J].

Bobkov, SG ;

Gentil, I ;

Ledoux, M .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2001, 80 (07) :669-696

[2] Exponential integrability and transportation cost related to logarithmic sobolev inequalities [J].

Bobkov, SG ;

Götze, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 163 (01) :1-28

[3] On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case [J].

Delarue, F .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 99 (02) :209-286

[4] Transportation cost-information inequalities and applications to random dynamical systems and diffusions [J].

Djellout, H ;

Guillin, A ;

Wu, L .

ANNALS OF PROBABILITY, 2004, 32 (3B) :2702-2732

[5] Monge-Kantorovitch measure transportation and Monge-Ampere equation on Wiener space [J].

Feyel, D ;

Üstünel, AS .

PROBABILITY THEORY AND RELATED FIELDS, 2004, 128 (03) :347-385

[6]

Feyel D., 2002, CRAS SERIE, VI, P1025

[7]

Hamadene S, 1996, ANN I H POINCARE-PR, V32, P645

[8] Liquidity, Risk Measures, and Concentration of Measure [J].

Lacker, Daniel .

MATHEMATICS OF OPERATIONS RESEARCH, 2018, 43 (03) :813-837

[9] ADAPTED SOLUTION OF A BACKWARD STOCHASTIC DIFFERENTIAL-EQUATION [J].

PARDOUX, E ;

PENG, SG .

SYSTEMS & CONTROL LETTERS, 1990, 14 (01) :55-61

[10]

stnel A., 2012, STOCHASTIC ANAL RELA, P203

← 1 2 →