LAUSR

Equidistribution for Nonuniformly Expanding Dynamical Systems, and Application to the Almost Sure Invariance Principle

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0 Published in 2017 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-017-3062-z

Abstract: Let $${T : M \to M}$$T:M→M be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let $${v : M \to \mathbb{R}^d}$$v:M→Rd be an observable and $${v_n = \sum_{k=0}^{n-1} v \circ T^k}$$vn=∑k=0n-1v∘Tk denote… read more here.

Keywords: invariance principle; sure invariance; almost sure; expanding dynamical ... See more keywords

Positive definiteness and the Stolarsky invariance principle

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1 Published in 2022 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2022.126220

Abstract: In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a K-invariant measure μ with full support, we show that conditional positive definiteness of… read more here.

Keywords: energy; positive definiteness; definiteness; stolarsky invariance ... See more keywords

Invariance principle for biased bootstrap random walks

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1 Published in 2019 at "Stochastic Processes and their Applications"

DOI: 10.1016/j.spa.2018.03.022

Abstract: Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random… read more here.

Keywords: cellular automata; process; sequence; invariance principle ... See more keywords

The invariance principle in baseball: new evidence

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1 Published in 2018 at "Applied Economics"

DOI: 10.1080/00036846.2017.1403561

Abstract: ABSTRACT This article considers the change in revenue sharing in Major League Baseball that occurred prior to the 2007 season and its effects on parity via its effects on marginal revenues. Based on the results… read more here.

Keywords: baseball; invariance principle; market; evidence ... See more keywords

Invariance principle and rigidity of high entropy measures

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0 Published in 2018 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/7278

Abstract: A deep analysis of the Lyapunov exponents for stationary sequence of matrices going back to Furstenberg, for more general linear cocycles by Ledrappier, and generalized to the context of non-linear cocycles by Avila and Viana,… read more here.

Keywords: invariance principle; principle; high entropy; principle rigidity ... See more keywords

A Nonsmooth Hybrid Invariance Principle Applied to Robust Event-Triggered Design

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1 Published in 2019 at "IEEE Transactions on Automatic Control"

DOI: 10.1109/tac.2018.2863188

Abstract: We first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone, and complete jumping solutions cannot jump outside the jump and flow… read more here.

Keywords: event triggered; nonsmooth hybrid; invariance principle; hybrid invariance ... See more keywords

Application of LaSalle’s Invariance Principle on Polynomial Differential Equations Using Quantifier Elimination

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1 Published in 2022 at "IEEE Transactions on Automatic Control"

DOI: 10.1109/tac.2021.3103887

Abstract: LaSalle’s invariance principle is a commonly used extension of Lyapunov’s second method to study asymptotic stability of nonlinear systems. If the system can be written in polynomial form, the examination can be automated using algebraic… read more here.

Keywords: lasalle invariance; invariance principle; quantifier elimination;

Invariance principle via orthomartingale approximation

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0 Published in 2018 at "Stochastics and Dynamics"

DOI: 10.1142/s0219493718500430

Abstract: We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences.… read more here.

Keywords: via orthomartingale; approximation; invariance principle; condition ... See more keywords