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The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
The Kullback-Liebler Divergence as a Lyapunov Function for Incentive Based Game Dynamics
The Kullback-Liebler Divergence Lyapunov Function Incentive Game Dynamics Dynamical Systems
2012/7/9
It has been shown that the Kullback-Leibler divergence is a Lyapunov function for the replicator equations at evolutionary stable states, or ESS. In this paper we extend the result to a more general c...
Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Orlicz-Hardy Spaces Associated with Divergence Operators on Unbounded Strongly Lipschitz Domains of $\mathbb{R}^n$
Orlicz-Hardy space divergence form elliptic operator strongly Lipschitz domain Neumann boundary condition Gaussian property
2011/9/9
Abstract: Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\...
A procedure for the change point problem in parametric models based on phi-divergence test-statistics
Change point Information criterion Divergence Wald test-statistic General distributions
2011/8/25
Abstract: This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on ge...
Change point analysis of an exponential model based on Phi-divergence test-statistics: simulated critical points case
Change point Exponential model Likelihood ratio test Power-divergence test statistic
2011/8/25
Abstract: Recently Batsidis \textit{et al.} (2011) have presented a new procedure based on divergence measures for testing the hypothesis of the existence of a change point in exponential populations....
Multiplicity-Free Representations of Divergence-Free Lie Algebras
divergence-free Lie algebra Cartan type graded modules irreducible modules
2011/2/21
Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are
Lie algebras of volume-preserving transformation groups. They are simple in generic case.
Dokovic and Zhao fo...
The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up.
An $f$-divergence approach for optimal portfolios in exponential Levy models
f-divergence exponential Levy models optimal portfolio
2011/1/21
We present a unified approach to get explicit formulas for utility maximising strategies in Exponential Levy models. This approach is related to f-divergence minimal martingale measures and based on a...
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which shou...
Shadowing, expansiveness and stability of divergence-free vector fields
divergence-free vector fields math
2010/11/22
Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions:
1. X is in the C1-interior of th...
The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
The Harnack inequality related properties elliptic
2010/11/15
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations
Free energy Kullback-Leibler divergence
2010/11/17
The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecula...
Bounds for Entropy and Divergence for Distributions over a Two-Element Set
Entropy divergence Pinsker's inequality
2008/7/2
Three results dealing with probability distributions (p,q) over a two-element set are presented. The two first give bounds for the entropy function H(p,q) and are referred to as the logarithmic and th...