The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Feng Yang - One of the best experts on this subject based on the ideXlab platform.
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new h state estimation criteria of delayed static neural networks via the lyapunov krasovskii functional with Negative Definite terms
Neural Networks, 2020Co-Authors: Yan Liang, Feisheng Yang, Feng YangAbstract:Abstract In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov–Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with Negative Definite terms is proposed. Based on the third-order Bessel–Legendre (B–L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H ∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
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New H∞ state estimation criteria of delayed static neural networks via the Lyapunov-Krasovskii functional with Negative Definite terms.
Neural networks : the official journal of the International Neural Network Society, 2019Co-Authors: Yan Liang, Feisheng Yang, Feng YangAbstract:Abstract In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov–Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with Negative Definite terms is proposed. Based on the third-order Bessel–Legendre (B–L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H ∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
Niels Jacob - One of the best experts on this subject based on the ideXlab platform.
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Aspects of Micro-Local Analysis and Geometry in the Study of Lévy-Type Generators
Open Quantum Systems, 2019Co-Authors: Niels Jacob, Elian O. T. RhindAbstract:Generators of Feller processes are pseudo-differential operators with Negative Definite symbols, thus they are objects of micro-local analysis. Continuous Negative Definite functions (and symbols) give often raise to metrics and these metrics are important to understand, for example, transition functions of certain Feller processes. In this survey we outline some of the more recent results and ideas while at the same time we long to introduce into the field.
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Q-matrices as pseudo-differential operators with Negative Definite symbols
Mathematische Nachrichten, 2012Co-Authors: Kristian P Evans, Niels JacobAbstract:Operators induced by Q-matrices on are shown to satisfy the positive maximum principle and to have a representation as a pseudo-differential operator with symbol which is with respect to the co-variable Negative Definite (in the sense of Schoenberg). This observation leads already towards a more geometric interpretation of the transition matrix of the associated Markov chain.
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A Parameter-Dependent Symbolic Calculus for Pseudo-Differential Operators with Negative-Definite Symbols
Journal of the London Mathematical Society, 2004Co-Authors: Niels Jacob, A. G. TokarevAbstract:Hoh's calculus for pseudo-differential operators with Negative-Definite symbols is extended to the case of parameter-dependent symbols. Then this parameter-dependent calculus is applied to the study of subordinate sub-Markovian semigroups.
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pseudo differential operators with Negative Definite functions as symbol applications in probability theory and mathematical physics
1992Co-Authors: Niels JacobAbstract:We discuss pseudo differential operators a(x,D) with a symbol a(x,ξ) which is with respect to ξ a continuous Negative Definite function. Such operators do occur in probability theory and mathematical physics.
Yan Liang - One of the best experts on this subject based on the ideXlab platform.
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new h state estimation criteria of delayed static neural networks via the lyapunov krasovskii functional with Negative Definite terms
Neural Networks, 2020Co-Authors: Yan Liang, Feisheng Yang, Feng YangAbstract:Abstract In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov–Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with Negative Definite terms is proposed. Based on the third-order Bessel–Legendre (B–L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H ∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
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New H∞ state estimation criteria of delayed static neural networks via the Lyapunov-Krasovskii functional with Negative Definite terms.
Neural networks : the official journal of the International Neural Network Society, 2019Co-Authors: Yan Liang, Feisheng Yang, Feng YangAbstract:Abstract In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov–Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with Negative Definite terms is proposed. Based on the third-order Bessel–Legendre (B–L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H ∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
Laurens De Haan - One of the best experts on this subject based on the ideXlab platform.
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Stationary max-stable fields associated to Negative Definite functions.
The Annals of Probability, 2009Co-Authors: Zakhar Kabluchko, Martin Schlather, Laurens De HaanAbstract:Let Wi, i∈ℕ, be independent copies of a zero-mean Gaussian process {W(t), t∈ℝd} with stationary increments and variance σ2(t). Independently of Wi, let ∑i=1∞δUi be a Poisson point process on the real line with intensity e−y dy. We show that the law of the random family of functions {Vi(⋅), i∈ℕ}, where Vi(t)=Ui+Wi(t)−σ2(t)/2, is translation invariant. In particular, the process η(t)=⋁i=1∞Vi(t) is a stationary max-stable process with standard Gumbel margins. The process η arises as a limit of a suitably normalized and rescaled pointwise maximum of n i.i.d. stationary Gaussian processes as n→∞ if and only if W is a (nonisotropic) fractional Brownian motion on ℝd. Under suitable conditions on W, the process η has a mixed moving maxima representation.
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stationary max stable fields associated to Negative Definite functions
arXiv: Probability, 2008Co-Authors: Zakhar Kabluchko, Martin Schlather, Laurens De HaanAbstract:Let $W_i,i\in{\mathbb{N}}$, be independent copies of a zero-mean Gaussian process $\{W(t),t\in{\mathbb{R}}^d\}$ with stationary increments and variance $\sigma^2(t)$. Independently of $W_i$, let $\sum_{i=1}^{\infty}\delta_{U_i}$ be a Poisson point process on the real line with intensity $e^{-y} dy$. We show that the law of the random family of functions $\{V_i(\cdot),i\in{\mathbb{N}}\}$, where $V_i(t)=U_i+W_i(t)-\sigma^2(t)/2$, is translation invariant. In particular, the process $\eta(t)=\bigvee_{i=1}^{\infty}V_i(t)$ is a stationary max-stable process with standard Gumbel margins. The process $\eta$ arises as a limit of a suitably normalized and rescaled pointwise maximum of $n$ i.i.d. stationary Gaussian processes as $n\to\infty$ if and only if $W$ is a (nonisotropic) fractional Brownian motion on ${\mathbb{R}}^d$. Under suitable conditions on $W$, the process $\eta$ has a mixed moving maxima representation.
Paul Ressel - One of the best experts on this subject based on the ideXlab platform.
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Negative Definite and Schoenberg functions on commutative hypergroups
Journal of the Australian Mathematical Society, 2005Co-Authors: Walter R. Bloom, Paul ResselAbstract:In this paper we investigate when Negative Definite functions on commutative hypergroups satisfy the Schoenberg criterion.
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Representations of Negative Definite functions on polynomial hypergroups
Archiv der Mathematik, 2002Co-Authors: Walter R. Bloom, Paul ResselAbstract:We investigate the relationship between polynomial hypergroups and the usual semigroup structure on the non-Negative integers.
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Positive Definite and related functions on hypergroups
Canadian Journal of Mathematics, 1991Co-Authors: Walter R. Bloom, Paul ResselAbstract:In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Levy-Khinchin representation for Negative Definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive Definite and Negative Definite functions on hypergroups.
