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

DOI10.1007/s11425-013-4569-1zbMath1273.60068arXiv1310.5932OpenAlexW2261553212MaRDI QIDQ362535

Xiliang Fan

Publication date: 22 August 2013

Published in: Science China. Mathematics, Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5932

zbMATH Keywords

stochastic differential equationHarnack inequalityfractional Brownian motioncouplingHarnack inequalities

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Markov semigroups and applications to diffusion processes (47D07) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

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Cites Work

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• Harnack inequality and derivative formula for SDE driven by fractional Brownian motion
• Harnack inequality and applications for stochastic evolution equations with monotone drifts
• Degenerate Fokker-Planck equations: Bismut formula, gradient estimate and Harnack inequality
• Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jump
• Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation
• Harnack inequalities on manifolds with boundary and applications
• Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
• Harnack inequalities for functional SDEs with multiplicative noise and applications
• Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds
• Harnack inequality for functional SDEs with bounded memory
• Integration with respect to fractal functions and stochastic calculus. I
• Differential equations driven by rough signals
• Stochastic analysis of the fractional Brownian motion
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• Harnack and functional inequalities for generalized Mehler semigroups.
• On the small time asymptotics of diffusion processes on path groups
• Hypercontractivity of Hamilton-Jacobi equations.
• Differential equations driven by fractional Brownian motion
• Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Derivative formulas and gradient estimates for SDEs driven by \(\alpha\)-stable processes
• Harnack inequality and applications for stochastic generalized porous media equations
• Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups
• Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below
• Regularization of differential equations by fractional noise.
• An inequality of the Hölder type, connected with Stieltjes integration
• Heat Kernel Estimates with Application to Compactness of Manifolds
• The Malliavin Calculus and Related Topics
• LOG-HARNACK INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS CONSEQUENCES
• Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
• Harnack Inequalities for Stochastic Partial Differential Equations
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Stochastic calculus with respect to Gaussian processes

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