The Experts below are selected from a list of 4092 Experts worldwide ranked by ideXlab platform
Feng-yu Wang - One of the best experts on this subject based on the ideXlab platform.
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asymptotic log Harnack Inequality and applications for stochastic systems of infinite memory
Stochastic Processes and their Applications, 2019Co-Authors: Feng-yu Wang, Jianhai Bao, Chenggui YuanAbstract:Abstract The asymptotic log-Harnack Inequality is established for several kinds of models on stochastic differential systems with infinite memory: non-degenerate SDEs, neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate, uniqueness of the invariant probability measure, asymptotic gradient estimate (hence, asymptotically strong Feller property), as well as asymptotic irreducibility.
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Coupling by Change of Measure, Harnack Inequality and Hypercontractivity
Stochastic Partial Differential Equations and Related Fields, 2018Co-Authors: Feng-yu WangAbstract:The coupling method is a powerful tool in analysis of stochastic processes. To make the coupling successful before a given time, it is essential that two marginal processes are constructed under different probability measures. We explain the main idea of establishing Harnack inequalities for Markov semigroups using these new type couplings, and apply the coupling and Harnack Inequality to the study of hypercontractivity of Markov semigroups.
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asymptotic log Harnack Inequality and applications for stochastic systems of infinite memory
arXiv: Probability, 2017Co-Authors: Feng-yu Wang, Jianhai Bao, Chenggui YuanAbstract:The asymptotic log-Harnack Inequality is established for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the invariant probability measure; asymptotic gradient estimate and hence, asymptotically strong Feller property; and asymptotic irreducibilty.
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Harnack Inequality and applications for infinite dimensional gem processes
arXiv: Probability, 2014Co-Authors: Shui Feng, Feng-yu WangAbstract:The dimension-free Harnack Inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in \cite{FW} to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev Inequality which strengthens the log-Sobolev Inequality derived in \cite{FW}. To prove the main results, explicit Harnack Inequality and super Poincar\'e Inequality are established for the one-dimensional Wright-Fisher diffusion processes. The main tool of the study is the coupling by change of measures.
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log Harnack Inequality for mild solutions of spdes with multiplicative noise
Stochastic Processes and their Applications, 2014Co-Authors: Feng-yu Wang, Tusheng ZhangAbstract:Due to technical reasons, existing results concerning Harnack type inequalities for SPDEs with multiplicative noise apply only to the case where the coefficient in the noise term is a Hilbert–Schmidt perturbation of a constant bounded operator. In this paper we obtained gradient estimates, log-Harnack Inequality for mild solutions of general SPDEs with multiplicative noise whose coefficient is even allowed to be unbounded which cannot be Hilbert–Schmidt. Applications to stochastic reaction–diffusion equations driven by space–time white noise are presented.
Zoran Vondraček - One of the best experts on this subject based on the ideXlab platform.
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parabolic Harnack Inequality for the mixture of brownian motion and stable process
Tohoku Mathematical Journal, 2007Co-Authors: Renming Song, Zoran VondračekAbstract:Let X be a mixture of independent Brownian motion and symmetric stable process. In this paper we establish sharp bounds for transition density of X, and prove a parabolic Harnack Inequality for nonnegative parabolic functions of X.
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green function estimates and Harnack Inequality for subordinate brownian motions
Potential Analysis, 2006Co-Authors: Murali Rao, Renming Song, Zoran VondračekAbstract:Let X be a Levy process in\(\mathbb{R}^{d} \), \(d \geqslant 3\), obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Levy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Levy measure of the subordinator we prove that the Harnack Inequality is valid for the nonnegative harmonic functions of X.
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Harnack Inequality for some discontinuous markov processes with a diffusion part
Glasnik Matematicki, 2005Co-Authors: Renming Song, Zoran VondračekAbstract:In this paper we establish a Harnack Inequality for nonnegative harmonic functions of some discontinuous Markov processes with a diffusion part.
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Harnack Inequality for some classes of Markov processes
Mathematische Zeitschrift, 2003Co-Authors: Renming Song, Zoran VondračekAbstract:In this paper we establish a Harnack Inequality for nonnegative harmonic functions of some classes of Markov processes with jumps.
Ki-ahm Lee - One of the best experts on this subject based on the ideXlab platform.
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Parabolic Harnack Inequality of viscosity solutions on Riemannian manifolds
Journal of Functional Analysis, 2014Co-Authors: Soojung Kim, Ki-ahm LeeAbstract:Abstract We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold M with the sectional curvature bounded from below by − κ for κ ≥ 0 . In the elliptic case, Wang and Zhang [24] recently extended the results of [5] to nonlinear elliptic equations in nondivergence form on such M , where they obtained the Harnack Inequality for classical solutions. We establish the Harnack Inequality for nonnegative viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on M . The Harnack Inequality of nonnegative viscosity solutions to the elliptic equations is also proved.
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Parabolic Harnack Inequality of viscosity solutions on Riemannian manifolds
arXiv: Analysis of PDEs, 2013Co-Authors: Soojung Kim, Ki-ahm LeeAbstract:We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold $M$, with the sectional curvature bounded from below by $-\kappa$ for $\kappa\geq 0$. In the elliptic case, Wang and Zhang \cite{WZ} recently extended the results of \cite{Ca} to nonlinear elliptic equations in nondivergence form on such $M$, where they obtained the Harnack Inequality for classical solutions. We establish the Harnack Inequality for nonnegative {\it viscosity solutions} to nonlinear uniformly {\it parabolic equations} in nondivergence form on $M$. The Harnack Inequality of nonnegative viscosity solutions to the elliptic equations is also proved.
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Harnack Inequality for nondivergent parabolic operators on Riemannian manifolds
Calculus of Variations and Partial Differential Equations, 2013Co-Authors: Seick Kim, Soojung Kim, Ki-ahm LeeAbstract:We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabre proved a global Krylov-Safonov Harnack Inequality under the assumption that the sectional curvature of the underlying manifold is nonnegative. Later, Kim improved Cabre’s result by replacing the curvature condition by a certain condition on the distance function. Assuming essentially the same condition introduced by Kim, we establish Krylov-Safonov Harnack Inequality for nonnegative solutions of the non-divergent parabolic equation. This, in particular, gives a new proof for Li-Yau Harnack Inequality for positive solutions to the heat equation in a manifold with nonnegative Ricci curvature.
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Harnack Inequality for nondivergent parabolic operators on Riemannian manifolds
Calculus of Variations and Partial Differential Equations, 2013Co-Authors: Seick Kim, Soojung Kim, Ki-ahm LeeAbstract:We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabr\'e proved a global Krylov-Safonov Harnack Inequality under the assumption that the sectional curvature of the underlying manifold is nonnegative. Later, Kim improved Cabr\'e's result by replacing the curvature condition by a certain condition on the distance function. Assuming essentially the same condition introduced by Kim, we establish Krylov-Safonov Harnack Inequality for nonnegative solutions of the non-divergent parabolic equation. This, in particular, gives a new proof for Li-Yau Harnack Inequality for positive solutions to the heat equation in a manifold with nonnegative Ricci curvature.Comment: 34 pages, 1 figure, 1 reference adde
Mihai Băileşteanu - One of the best experts on this subject based on the ideXlab platform.
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A Harnack Inequality for the parabolic Allen–Cahn equation
Annals of Global Analysis and Geometry, 2016Co-Authors: Mihai BăileşteanuAbstract:We prove a differential Harnack Inequality for the solution of the parabolic Allen–Cahn equation \( \frac{\partial f}{\partial t}=\triangle f-(f^3-f)\) on a closed n-dimensional manifold. As a corollary, we find a classical Harnack Inequality. We also formally compare the standing wave solution to a gradient estimate of Modica from the 1980s for the elliptic equation.
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A Harnack Inequality for the parabolic Allen-Cahn equation
arXiv: Differential Geometry, 2015Co-Authors: Mihai BăileşteanuAbstract:We prove a differential Harnack Inequality for the solution of the parabolic Allen-Cahn equation $ \frac{\partial f}{\partial t}=\triangle f-(f^3-f)$ on a closed n-dimensional manifold. As a corollary we find a classical Harnack Inequality. We also formally compare the standing wave solution to a gradient estimate of Modica from the 1980s for the elliptic equation.
Cyril Imbert - One of the best experts on this subject based on the ideXlab platform.
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The weak Harnack Inequality for the Boltzmann equation without cut-off
Journal of the European Mathematical Society, 2020Co-Authors: Cyril Imbert, Luis SilvestreAbstract:We obtain the weak Harnack Inequality and Hölder estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cutoff can be written in this form and satisfies our assumptions provided that the mass density is bounded away from vacuum and mass, energy and entropy densities are bounded above. As a consequence, we derive a local Hölder estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cutoff .
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the weak Harnack Inequality for the boltzmann equation without cut off
arXiv: Analysis of PDEs, 2016Co-Authors: Cyril Imbert, Luis SilvestreAbstract:In this paper, we obtain the weak Harnack Inequality and Holder estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this form and satisfies our assumptions provided that the mass density is bounded away from vacuum and mass, energy and entropy densities are bounded above. As a consequence, we derive a local Holder estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cut-off.
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alexandroff bakelman pucci estimate and Harnack Inequality for degenerate singular fully non linear elliptic equations
Journal of Differential Equations, 2011Co-Authors: Cyril ImbertAbstract:In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when ``the gradient is small''. Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack Inequality for viscosity solutions of such degenerate elliptic equations.
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Alexandroff-Bakelman-Pucci estimate and Harnack Inequality for degenerate/singular fully non-linear elliptic equations
Journal of Differential Equations, 2011Co-Authors: Cyril ImbertAbstract:In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when ``the gradient is small''. Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack Inequality for viscosity solutions of such degenerate elliptic equations.
