The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
David M. Mason - One of the best experts on this subject based on the ideXlab platform.
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A Universal One-Sided Law of the Iterated Logarithm
The Annals of Probability, 1994Co-Authors: David M. MasonAbstract:We prove that the Lim Inf of suitably normalized sums of i.i.d. nonnegative and nondegenerate random variables can with probability 1 only be a constant between -2 1/2 and 0. Moreover, we show that each value within this range is attainable by an appropriate choice of the underlying common distribution function.
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A Universal Chung-Type Law of the Iterated Logarithm
The Annals of Probability, 1994Co-Authors: Uwe Einmahl, David M. MasonAbstract:Let X 1 , X 2 ,..., be a sequence of independent and identically distributed random variables. We find sequences of norming and centering constants α n and β n such that a universal Chung-type law of the iterated logarithm holds, namely, Lim Inf n→ ∞ max 1 ≤k≤ n S k -kβ n /α n
Alessandro Astolfi - One of the best experts on this subject based on the ideXlab platform.
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Invariance-like theorems and weak convergence properties
IEEE Transactions on Automatic Control, 2016Co-Authors: Giordano Scarciotti, Laurent Praly, Alessandro AstolfiAbstract:Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “Lim Inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “Lim Inf” Matrosov and Small-gain theorems and are based on a “Lim Inf” Barbalat's Lemma. Additional technical assumptions to have “Lim” convergence are given: the “Lim Inf”/“Lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
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Invariance-Like Theorems and “Lim Inf” Convergence Properties
IEEE Transactions on Automatic Control, 2016Co-Authors: Giordano Scarciotti, Laurent Praly, Alessandro AstolfiAbstract:Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “Lim Inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “Lim Inf” Matrosov and Small-gain theorems and are based on a “Lim Inf” Barbalat's Lemma. Additional technical assumptions to have “Lim” convergence are given: the “Lim Inf”/“Lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
Jean-françois Raskin - One of the best experts on this subject based on the ideXlab platform.
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CSL-LICS - Secure equilibria in weighted games
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM IEEE Symp, 2014Co-Authors: Véronique Bruyère, Noémie Meunier, Jean-françois RaskinAbstract:We consider two-player non zero-sum Infinite duration games played on weighted graphs. We extend the notion of secure equilibrium introduced by Chatterjee et al., from the Boolean setting to this quantitative setting. As for the Boolean setting, our notion of secure equilibrium refines the classical notion of Nash equilibrium. We prove that secure equilibria always exist in a large class of weighted games which includes common measures like sup, Inf, Lim sup, Lim Inf, mean-payoff, and discounted sum. Moreover we show that one can synthesize finite-memory strategy profiles with few memory. We also prove that the constrained existence problem for secure equilibria is decidable for sup, Inf, Lim sup, Lim Inf and mean-payoff measures. Our solutions rely on new results for zero-sum quantitative games with lexicographic objectives that are interesting on their own right.
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Secure Equilibria in Weighted Games
arXiv: Computer Science and Game Theory, 2014Co-Authors: Véronique Bruyère, Noémie Meunier, Jean-françois RaskinAbstract:We consider two-player non zero-sum Infinite duration games played on weighted graphs. We extend the notion of secure equilibrium introduced by Chatterjee et al., from the Boolean setting to this quantitative setting. As for the Boolean setting, our notion of secure equilibrium refines the classical notion of Nash equilibrium. We prove that secure equilibria always exist in a large class of weighted games which includes common measures like sup, Inf, Lim sup, Lim Inf, mean-payoff, and discounted sum. Moreover we show that one can synthesize finite-memory strategy profiles with few memory. We also prove that the constrained existence problem for secure equilibria is decidable for sup, Inf, Lim sup, Lim Inf and mean-payoff measures. Our solutions rely on new results for zero-sum quantitative games with lexicographic objectives that are interesting on their own right.
Sudhir Mishra - One of the best experts on this subject based on the ideXlab platform.
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A NEW POINT IN LAGRANGE SPECTRUM
International Journal of Number Theory, 2013Co-Authors: Kalika Prasad, Hrishikesh Mahato, Sudhir MishraAbstract:Let I denote the set of all irrational numbers, θ ∈ I, and simple continued fraction expansion of θ be [a0, a1, …, an, …]. Then a0 is an integer and {an}n≥1 is an Infinite sequence of positive integers. Let Mn(θ) = [0, an, an-1, …, a1] + [an+1, an+2, …]. Then the set of numbers {Lim sup Mn(θ) ∣ θ ∈ I} is called the Lagrange Spectrum 𝔏. Notably 3 is the first cluster point of 𝔏. Essentially Lim Inf 𝔏 or . Perron [Uber die approximation irrationaler Zahlen durch rationale, I, S.-B. Heidelberg Akad. Wiss., Abh. 4 (1921) 17 pp; Uber die approximation irrationaler Zahlen durch rationale, II, S.-B. Heidelberg Akad. Wiss., Abh.8 (1921) 12 pp.] has found that Lim Inf{Lim sup Mn(θ) ∣ θ = [a0, a1, a2, …, an, …] and . This article forwards the value of Lim Inf{Lim sup Mn(θ) ∣ θ = [a0, a1, …, an, …] and an ≥ 4 frequently}, a long awaited cluster point of Lagrange Spectrum.
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A NEW POINT IN LAGRANGE SPECTRUM
International Journal of Number Theory, 2012Co-Authors: K. C. Prasad, Hrishikesh Mahato, Sudhir MishraAbstract:Let I denote the set of all irrational numbers, θ ∈ I, and simple continued fraction expansion of θ be [a0, a1, …, an, …]. Then a0 is an integer and {an}n≥1 is an Infinite sequence of positive integers. Let Mn(θ) = [0, an, an-1, …, a1] + [an+1, an+2, …]. Then the set of numbers { Lim sup Mn(θ) ∣ θ ∈ I} is called the Lagrange Spectrum
Giordano Scarciotti - One of the best experts on this subject based on the ideXlab platform.
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Invariance-like theorems and weak convergence properties
IEEE Transactions on Automatic Control, 2016Co-Authors: Giordano Scarciotti, Laurent Praly, Alessandro AstolfiAbstract:Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “Lim Inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “Lim Inf” Matrosov and Small-gain theorems and are based on a “Lim Inf” Barbalat's Lemma. Additional technical assumptions to have “Lim” convergence are given: the “Lim Inf”/“Lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
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Invariance-Like Theorems and “Lim Inf” Convergence Properties
IEEE Transactions on Automatic Control, 2016Co-Authors: Giordano Scarciotti, Laurent Praly, Alessandro AstolfiAbstract:Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “Lim Inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “Lim Inf” Matrosov and Small-gain theorems and are based on a “Lim Inf” Barbalat's Lemma. Additional technical assumptions to have “Lim” convergence are given: the “Lim Inf”/“Lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.