Scan Science and Technology
Contact Leading Edge Experts & Companies
Analyticity
The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
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, 2019CoAuthors: Vladislav B Tadic, Arnaud DoucetAbstract:The Analyticity of the entropy and relative entrentropy rates of continuousstate 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, 2018CoAuthors: Vladislav B Tadic, Arnaud DoucetAbstract:The Analyticity of the entropy and relative entrentropy rates of continuousstate 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, 2019CoAuthors: Vladislav B Tadic, Arnaud DoucetAbstract:The Analyticity of the entropy and relative entropy rates of continuousstate 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, 2018CoAuthors: Vladislav B Tadic, Arnaud DoucetAbstract:The Analyticity of the entropy and relative entropy rates of continuousstate 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, 2016CoAuthors: Shangkun WengAbstract:Abstract We address the Analyticity and large time decay rates for strong solutions of the HallMHD 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, 2014CoAuthors: Shangkun WengAbstract:We address the Analyticity and large time decay rates for strong solutions of the HallMHD 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, 2010CoAuthors: Igor Kukavica, Vlad VicolAbstract: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 realAnalyticity 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 subanalytic Gevreyclass regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevreyclass regularity.

the domain of Analyticity of solutions to the three dimensional euler equations in a half space
arXiv: Analysis of PDEs, 2010CoAuthors: Igor Kukavica, Vlad VicolAbstract: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 realAnalyticity 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 subanalytic Gevreyclass regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevreyclass regularity.

on the radius of Analyticity of solutions to the three dimensional euler equations
Proceedings of the American Mathematical Society, 2008CoAuthors: Igor Kukavica, Vlad VicolAbstract:We address the problem of Analyticity of smooth solutions u of the incompressible Euler equations. If the initial datum is realanalytic, the solution remains realanalytic as long as f t 0 ∥∇u(·, s)∥ L∞ ds < ∞. Using a Gevreyclass 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, 2020CoAuthors: Hongjie Dong, Qi S ZhangAbstract: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 illposed 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 NavierStokes equations in the whole space. There are many long established Analyticity results for the NavierStokes equations. See for example [17] and [10] for spatial and time Analyticity in certain integral sense, [4] for pointwise spacetime 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.