The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform

Benjamin Havret - One of the best experts on this subject based on the ideXlab platform.

Tomasz Grzywny - One of the best experts on this subject based on the ideXlab platform.

  • L{\'e}vy processes: concentration function and heat kernel bounds
    arXiv: Probability, 2019
    Co-Authors: Tomasz Grzywny, Karol Szczypkowski
    Abstract:

    We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the Characteristic Exponent repeatedly used in the literature of the subject are equivalent to the behaviour of the maximum of the density as a function of time variable. We also prove qualitative lower estimates under mild assumptions on the corresponding jump measure and the Characteristic Exponent.

  • On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy Processes
    Potential Analysis, 2014
    Co-Authors: Tomasz Grzywny
    Abstract:

    We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal Lévy process with the Characteristic Exponent ψ satisfying some scaling condition. We derive sharp estimates of the potential measure and capacity of balls, and further, under the assumption that ψ satisfies the lower scaling condition, sharp estimates of the potential kernel of the underlying process. This allows us to establish the Krylov–Safonov type estimate, which is the key ingredient in the approach of Bass and Levin, that we follow.

  • on harnack inequality and holder regularity for isotropic unimodal levy processes
    Potential Analysis, 2014
    Co-Authors: Tomasz Grzywny
    Abstract:

    We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal Levy process with the Characteristic Exponent ψ satisfying some scaling condition. We derive sharp estimates of the potential measure and capacity of balls, and further, under the assumption that ψ satisfies the lower scaling condition, sharp estimates of the potential kernel of the underlying process. This allows us to establish the Krylov–Safonov type estimate, which is the key ingredient in the approach of Bass and Levin, that we follow.

Federico Milano - One of the best experts on this subject based on the ideXlab platform.

  • viable computation of the largest lyapunov Characteristic Exponent for power systems
    IEEE PES Innovative Smart Grid Technologies Conference, 2018
    Co-Authors: Brendan Hayes, Federico Milano
    Abstract:

    Stochastic Differential Algebraic Equations (SDAEs) are used to model power systems. However, there is no universally accepted method to properly evaluate the stability of such models. The theoretical and numerical aspects of the computation of the largest Lyapunov Characteristic Exponent (LCE) for power systems with the inclusion of stochastic processes is discussed as a method to provide a measure of stability. A semi-implicit formulation of power systems is employed in order to exploit parallelism, sparsity and to have low memory requirements. Three case studies are considered, two based on the IEEE 14-bus system as well as a 1,479-bus model of the all island Irish transmission grid.

  • ISGT Europe - Viable Computation of the Largest Lyapunov Characteristic Exponent for Power Systems
    2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), 2018
    Co-Authors: Brendan Hayes, Federico Milano
    Abstract:

    Stochastic Differential Algebraic Equations (SDAEs) are used to model power systems. However, there is no universally accepted method to properly evaluate the stability of such models. The theoretical and numerical aspects of the computation of the largest Lyapunov Characteristic Exponent (LCE) for power systems with the inclusion of stochastic processes is discussed as a method to provide a measure of stability. A semi-implicit formulation of power systems is employed in order to exploit parallelism, sparsity and to have low memory requirements. Three case studies are considered, two based on the IEEE 14-bus system as well as a 1,479-bus model of the all island Irish transmission grid.

Nicolas Privault - One of the best experts on this subject based on the ideXlab platform.

  • laplace transform identities and measure preserving transformations on the lie wiener poisson spaces
    Journal of Functional Analysis, 2012
    Co-Authors: Nicolas Privault
    Abstract:

    Abstract Given a divergence operator δ on a probability space such that the law of δ ( h ) is infinitely divisible with Characteristic Exponent (0.1) h ↦ − 1 2 ∫ 0 ∞ h t 2 d t , or ∫ 0 ∞ ( e i h ( t ) − i h ( t ) − 1 ) d t , h ∈ L 2 ( R + ) , we derive a family of Laplace transform identities for the derivative ∂ E [ e λ δ ( u ) ] / ∂ λ when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Carleman–Fredholm determinant of a covariant derivative operator and the Characteristic Exponent (0.1) , in a general framework that includes the Wiener space, the path space over a Lie group, and the Poisson space. We use these expressions for measure characterization and to prove the invariance of transformations having a quasi-nilpotent covariant derivative, for Gaussian and other infinitely divisible distributions.

  • Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces
    Journal of Functional Analysis, 2012
    Co-Authors: Nicolas Privault
    Abstract:

    Abstract Given a divergence operator δ on a probability space such that the law of δ ( h ) is infinitely divisible with Characteristic Exponent (0.1) h ↦ − 1 2 ∫ 0 ∞ h t 2 d t , or ∫ 0 ∞ ( e i h ( t ) − i h ( t ) − 1 ) d t , h ∈ L 2 ( R + ) , we derive a family of Laplace transform identities for the derivative ∂ E [ e λ δ ( u ) ] / ∂ λ when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Carleman–Fredholm determinant of a covariant derivative operator and the Characteristic Exponent (0.1) , in a general framework that includes the Wiener space, the path space over a Lie group, and the Poisson space. We use these expressions for measure characterization and to prove the invariance of transformations having a quasi-nilpotent covariant derivative, for Gaussian and other infinitely divisible distributions.

Denis Kouamé - One of the best experts on this subject based on the ideXlab platform.

  • Reconstruction of ultrasound RF echoes modelled as stable random variables
    IEEE Transactions on Computational Imaging, 2015
    Co-Authors: Alin Achim, Adrian Basarab, George Tzagkarakis, Panagiotis Tsakalides, Denis Kouamé
    Abstract:

    This paper introduces a new technique for reconstruction of biomedical ultrasound images from simulated compressive measurements, based on modeling data with stable distributions. The proposed algorithm exploits two types of prior information: on one hand, our proposed approach is based on the observation that ultrasound RF echoes are best characterized statistically by alpha-stable distributions. On the other hand, through knowledge of the acquisition process, the support of the RF echoes in the Fourier domain can be easily inferred. Together, these two facts form the basis of an ℓp minimization approach that employs the iteratively reweighted least squares (IRLS) algorithm, but in which the parameter p is judiciously chosen, by relating it to the Characteristic Exponent of the underlying alpha-stable distributed data. We demonstrate, through Monte Carlo simulations, that the optimal value of the parameter p is just below that of the Characteristic Exponent α, which we estimate from the data. Our reconstruction results show that the proposed algorithm outperforms previously proposed reconstruction techniques, both visually and in terms of two objective evaluation measures.