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harnack inequality and derivative formula for SDE driven by fractional Brownian motion

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Science China Mathematics 2013年第3期56卷 515-524页

作者： FAN XiLiang School of Mathematical Sciences Beijing Normal University Department of Mathematics Anhui Normal University

In the paper, harnack inequality and derivative formula are established for stochastic differential equation driven by fractional Brownian motion with Hurst parameter H < 1/2. As applications, strong Feller property, ... 详细信息

In the paper, harnack inequality and derivative formula are established for stochastic differential equation driven by fractional Brownian motion with Hurst parameter H harnack inequality and entropy-cost inequality are given.

关键词： harnack inequality stochastic differential equation fractional Brownian motion

harnack inequality and Applications for SDEs Driven by G-Brownian Motion

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 627-635页

作者： Fen-fen YANG Center for Applied Mathematics Tianjin UniversityTianjin 300072China

In this paper,Wang's harnack and shift harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are *** results generalize the ones in the linear expectation ***,some application... 详细信息

关键词： harnack inequality shift harnack inequality stochastic differential equations G-Brownian motion G-expectation

harnack inequality and gradient estimate for functional G-SDEs with degenerate noise

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Probability, Uncertainty and Quantitative Risk 2022年第2期7卷 119-132页

作者： Fen-Fen Yang Department of Mathematics Shanghai UniversityShanghai 2004China

In this paper,the harnack and shift harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of ***,the gradient estimate for the associated nonlinear semigroup ... 详细信息

关键词： harnack inequality Gradient estimate Degenerate noise Functional G-SDEs

harnack inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion

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Journal of Partial Differential Equations 2017年第1期30卷 84-94页

作者： LIU Min XU Liping LI Zhi CHEN Zhong School of Information and Mathematics Yangtze UniversityJingzhou 434023China

In this paper, by using a semimartingale approximation of a fractional stochastic integration, the global harnack inequalities for stochastic retarded differential equations driven by fractional Brownian motion with Hurst parameter 0 〈 H 〈 1 are established. As applications, strong Feller property, log-harnack inequality and entropycost inequality are given.

关键词： Fractional Brownian motion harnack inequality strong Feller property.

Gradient Estimates and harnack inequality for a Nonlinear Parabolic Equation on Complete Manifolds

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Communications in Mathematics and Statistics 2013年第4期1卷 437-464页

作者： Jiaxian Wu Yi-Hu Yang Department of Mathematics Tongji UniversityShanghai 200092China Department of Mathematics Shanghai Jiao Tong UniversityShanghai 200240China

Let M be a noncompact complete Riemannian *** this paper,we consider the following nonlinear parabolic equation on M ut(x,t)=△u(x,t)+au(x,t)ln u(x,t)+bu^α(x,t).We prove a Li–Yau type gradient estimate for positive solutions to the above equation;as an application,we also derive the corresponding harnack *** results generalize the corresponding ones proved by Li(J Funct Anal 100:233–256,1991).

关键词： Gradient estimate Ricci curvature harnack inequality Nonlinear parabolic equation

An Improved harnack inequality for Dirichlet Eigenvalues of Abelian Homogeneous Graphs

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Journal of Mathematical Research with Applications 2014年第6期34卷 640-646页

作者： Shoudong MAN Department of Mathematics School of Information Renmin University of China

In this paper, we prove an improved harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. As a consequence, we derive a lower estimate for Dirichlet eigenvalues usin... 详细信息

关键词： Laplace operator harnack inequality eigenvalue estimate

A Note on harnack Type inequality for the Gaussian Curvature Flow

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 1-4页

作者： Cai-peng CHEN Hong-xin GUO Cheng-zhe ZHU Department of mathematics Wenzhou UniversityWenzhou 325035China

In this short note we present a new harnack expression for the Gaussian curvature flow, which is modeled from the shrinking self similiar solutions. As applications we give alternate proofs of Chow’s harnack inequali... 详细信息

关键词： Gaussian Curvature flow harnack inequality

Local Hamilton type Gradient Estimates and harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 539-546页

作者： Wen WANG Da-peng XIE Hui ZHOU School of Mathematics and Statistics Hefei Normal UniversityHefei 230601China

In this paper,we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation ut(x,t)=Δu(x,t)+au(x,t) ln u(x,t)+bu^(α)(x,t),on M×(-∞,∞) with α∈R,where a and b are *** ... 详细信息

关键词： nonlinear parabolic equation gradient estimate harnack inequality

harnack and HWI Inequalities on Infinite-Dimensional Spaces

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1195-1204页

作者： Jing Hai SHAO School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

In this paper, the dimensional-free harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.

关键词： harnack inequality loop groups HWI inequality abstract Wiener space Ornstein- Uhlenbeck semigroup