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Analyticity

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Arnaud Doucet – One of the best experts on this subject based on the ideXlab platform.

  • Analyticity of entropy rates of continuous state hidden markov models
    IEEE Transactions on Information Theory, 2019
    Co-Authors: Vladislav B Tadic, Arnaud Doucet
    Abstract:

    The Analyticity of the entropy and relative entrentropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the Analyticity of these rates is established for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several useful classes of hidden Markov models. These results are relevant for several theoretically and practically important problems arising in statistical inference, system identification and information theory.

  • Analyticity of entropy rates of continuous state hidden markov models
    arXiv: Information Theory, 2018
    Co-Authors: Vladislav B Tadic, Arnaud Doucet
    Abstract:

    The Analyticity of the entropy and relative entrentropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the Analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory.

Vladislav B Tadic – One of the best experts on this subject based on the ideXlab platform.

  • Analyticity of entropy rates of continuous state hidden markov models
    IEEE Transactions on Information Theory, 2019
    Co-Authors: Vladislav B Tadic, Arnaud Doucet
    Abstract:

    The Analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the Analyticity of these rates is established for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several useful classes of hidden Markov models. These results are relevant for several theoretically and practically important problems arising in statistical inference, system identification and information theory.

  • Analyticity of entropy rates of continuous state hidden markov models
    arXiv: Information Theory, 2018
    Co-Authors: Vladislav B Tadic, Arnaud Doucet
    Abstract:

    The Analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the Analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory.

Shangkun Weng – One of the best experts on this subject based on the ideXlab platform.

  • on Analyticity and temporal decay rates of solutions to the viscous resistive hall mhd system
    Journal of Differential Equations, 2016
    Co-Authors: Shangkun Weng
    Abstract:

    Abstract We address the Analyticity and large time decay rates for strong solutions of the Hall-MHD equations. By Gevrey estimates, we show that the strong solution with small initial date in H r ( R 3 ) with r > 5 2 becomes analytic immediately after t > 0 , and the radius of Analyticity will grow like t in time. Upper and lower bounds on the decay of higher order derivatives are also obtained, which extends the previous work by Chae and Schonbek (2013) [4] .

  • on Analyticity and temporal decay rates of solutions to the viscous resistive hall mhd system
    arXiv: Analysis of PDEs, 2014
    Co-Authors: Shangkun Weng
    Abstract:

    We address the Analyticity and large time decay rates for strong solutions of the Hall-MHD equations. By Gevrey estimates, we show that the strong solution with small initial date in $H^r(\mathbb{R}^3)$ with $r>\f 52$ becomes analytic immediately after $t>0$, and the radius of Analyticity will grow like $\sqrt{t}$ in time. Upper and lower bounds on the decay of higher order derivatives are also obtained, which extends the previous work by Chae and Schonbek (J. Differential Equations 255 (2013), 3971–3982).

Igor Kukavica – One of the best experts on this subject based on the ideXlab platform.

  • the domain of Analyticity of solutions to the three dimensional euler equations in a half space
    Discrete and Continuous Dynamical Systems, 2010
    Co-Authors: Igor Kukavica, Vlad Vicol
    Abstract:

    We address the problem of Analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-Analyticity radius of the solution $u(t)$ in terms of exp$\int_{0}^{t} $||$ \nabla u(s) $|| L∞ ds , improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.

  • the domain of Analyticity of solutions to the three dimensional euler equations in a half space
    arXiv: Analysis of PDEs, 2010
    Co-Authors: Igor Kukavica, Vlad Vicol
    Abstract:

    We address the problem of Analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-Analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t} \Vert \nabla u(s) \Vert_{L^\infty} ds}$, improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.

  • on the radius of Analyticity of solutions to the three dimensional euler equations
    Proceedings of the American Mathematical Society, 2008
    Co-Authors: Igor Kukavica, Vlad Vicol
    Abstract:

    We address the problem of Analyticity of smooth solutions u of the incompressible Euler equations. If the initial datum is real-analytic, the solution remains real-analytic as long as f t 0 ∥∇u(·, s)∥ L∞ ds < ∞. Using a Gevrey-class approach we obtain lower bounds on the radius of space Analyticity which depend algebraically on exp ∫ t 0 ∥∇u(·,s)∥ L∞ ds. In particular, we answer in the positive a question posed by Levermore and Oliver.

Qi S Zhang – One of the best experts on this subject based on the ideXlab platform.

  • time Analyticity for the heat equation and navier stokes equations
    Journal of Functional Analysis, 2020
    Co-Authors: Hongjie Dong, Qi S Zhang
    Abstract:

    Abstract We prove the Analyticity in time for solutions of two parabolic equations in the whole space, without any decaying or vanishing conditions. One of them involves solutions to the heat equation of exponential growth of order 2 on M. Here M is R d or a complete noncompact manifold with Ricci curvature bounded from below by a constant. An implication is a sharp solvability condition for the Cauchy problem of the backward heat equation, which is a well known ill-posed problem. Another implication is a sharp criteria for time Analyticity of solutions down to the initial time. The other pertains bounded mild solutions of the incompressible Navier-Stokes equations in the whole space. There are many long established Analyticity results for the Navier-Stokes equations. See for example [17] and [10] for spatial and time Analyticity in certain integral sense, [4] for pointwise space-time Analyticity of 3 dimensional solutions to the Cauchy problem, and also the pointwise time Analyticity results of [22] and [12] under zero boundary condition. Our result seems to be the first general pointwise time Analyticity result for the Cauchy problem for all dimensions, whose proof involves only real variable method. The proof involves a method of algebraically manipulating the integral kernel, which appears applicable to other evolution equations.