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  An effective Chabauty-Kim theorem 

  Balakrishnan, Jennifer; Dogra, Netan (Foundation Compositio Mathematica, 2019-06)

  The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We ...
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  Measuring the signal-to-noise ratio of a neuron 

  Czanner, Gabriela; Sarma, Sridevi V.; Ba, Demba; Eden, Uri T.; Wu, Wei; Eskandar, Emad; Lim, Hubert H.; Temereanca, Simona; Suzuki, Wendy A.; Brown, Emery N. (NATL ACAD SCIENCES, 2015-06-09)

  The signal-to-noise ratio (SNR), a commonly used measure of fidelity in physical systems, is defined as the ratio of the squared amplitude or variance of a signal relative to the variance of the noise. This definition is ...
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  Intermittency and infinite variance: the case of integrated supOU processes 

  Grahovac, Danijel; Leonenko, Nikolai N.; Taqqu, Murad S.

  SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. ...
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  Generalized Hermite processes, discrete chaos and limit theorems 

  Bai, Shuyang; Taqqu, Murad S. (ELSEVIER SCIENCE BV, 2014-04-01)

  We introduce a broad class of self-similar processes \{Z(t),t\ge 0\} called generalized Hermite process. They have stationary increments, are defined on a Wiener chaos with Hurst index H\in (1/2,1), and include Hermite ...
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  Convergence of long-memory discrete kth order Volterra processes 

  Bai, Shuyang; Taqqu, Murad S. (ELSEVIER SCIENCE BV, 2015-05-01)

  We obtain limit theorems for a class of nonlinear discrete-time processes X(n) called the kth order Volterra processes of order k. These are moving average kth order polynomial forms: X(n)=∑0
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  Large scale reduction principle and application to hypothesis testing 

  Clausel, Marianne; Roueff, Francois; Taqqu, Murad S. (INST MATHEMATICAL STATISTICS, 2015-01-01)

  Consider a non–linear function G(Xt) where Xt is a stationary Gaussian sequence with long–range dependence. The usual reduction principle states that the partial sums of G(Xt) behave asymptotically like the partial sums ...
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  Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes 

  Clausel, M.; Roueff, F.; Taqqu, Murad S.; Tudor, C. (EDP SCIENCES S A, 2014-01-01)

  We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior ...
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  Weak convergence of the empirical process of intermittent maps in L-2 under long-range dependence 

  Dedecker, Jerome; Dehling, Herold; Taqqu, Murad S. (WORLD SCIENTIFIC PUBL CO PTE LTD, 2015-06-01)

  We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square integrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove ...
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  Structure of the third moment of the generalized Rosenblatt distribution 

  Bai, Shuyang; Taqqu, Murad S. (ELSEVIER SCIENCE BV, 2014-11-01)

  The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel that defines the usual Rosenblatt distribution. ...
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  Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem 

  Taqqu, Murad S.; Leonenko, Nikolai N.; Terdik, Gyorgy (2018)

  We consider the problem of estimating the covariance function of an isotropic Gaussian stochastic field on the unit sphere using a single observation at each point of the discretized sphere. The spatial estimator of the ...

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