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Documents  Todd, Michael J. | enregistrements trouvés : 9

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Research talks;Probability and Statistics

We give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index $\alpha \in \left ( 0,4 \right )$; in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative denite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum. This is joint work with Richard A. Davis (Columbia NY) and Oliver Pfaffel (Munich). We give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index $\alpha \in \left ( 0,4 \right )$; in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance ...

62G32 ; 60G55

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- 341 p.
ISBN 978-0-8218-5121-0

Contemporary mathematics , 0114

Localisation : Collection 1er étage

optimisation # programmation linéaire

49DXX ; 65Kxx ; 90Cxx

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ISBN 978-0-306-41127-4

NATO conference series , 0013

Localisation : Colloque 1er étage (PORT)

algorithme du point fixe # application ligne de fond # convergence globale # déflation # fonction entière # homotopie lisse par morceau # méthode d'homotopie # méthode de continuation linéaire par morceau # problème de complémentarité linéaire # technique de suivi de chemin # économie

14F35 ; 55-06 ; 55M20 ; 55Pxx ; 90C33

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- x, 279 p.
ISBN 978-0-521-73970-2

London mathematical society lecture note series , 0363

Localisation : Collection 1er étage

algèbre commutative # calcul formel # analyse numérique

13-06 ; 13Pxx ; 37MXX ; 65PXX ; 00B25

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Research talks;Mathematics in Science and Technology;Probability and Statistics

Analysing heavy rainfall in France is complex due to the high number of weather stations and the complexity of weather system patterns over the French territory. This leads to computational issues and classical Extreme Value Theory (ETV) cannot be directly applied. To bypass the computational hurdles, we perform a dimension reduction approach, based on EVT concepts, to create independent regional clusters. Within each cluster, we propose a nonparametric approach for estimating the maxima dependence function.
This is a joint work with S. A. Padoan, G. Marcon, E. Bernard, M. Vrac, O. Mestre.
Analysing heavy rainfall in France is complex due to the high number of weather stations and the complexity of weather system patterns over the French territory. This leads to computational issues and classical Extreme Value Theory (ETV) cannot be directly applied. To bypass the computational hurdles, we perform a dimension reduction approach, based on EVT concepts, to create independent regional clusters. Within each cluster, we propose a ...

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Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

It is shown that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. The error terms are powers of logarithm of the radius and so is the size of the forbidden set which one has to exclude. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.

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Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

The Poisson limit theorem which appeared in 1837 seems to be the first law of rare events in probability. Various generalizations of it and estimates of errors of Poisson approximations were obtained in probability and more recently this became a popular topic in dynamics in the form of study of asymptotics of numbers of arrivals at small (shrinking) sets by a stochastic process or by a dynamical system. I will describe recent results on Poisson and compound Poisson asymptotics in a nonconventional setup, i.e. for numbers of events of multiple returns to shrinking sets, namely, for numbers of combined events of the type $\left \{ \omega : \xi \left ( jn,\omega\right )\in \Gamma_N,j = 1,...,\ell \right \},n\leq N$ where $\xi \left ( k,\omega \right )$ is defined as a stochastic process from the beginning or it is built from a dynamical system by writing $\xi \left ( k,\omega \right )=T^k\omega .$ We obtain an essentially complete description of possible limiting behaviors of distributions of numbers of multiple recurrencies to shrinking cylinders for $\psi $-mixing shifts. Some possible extensions and related questions will be discussed, as well. Most of the results were obtained jointly with my student Ariel Rapaport and some of them are new even for the widely studied single (conventional) recurrencies case.
Keywords : Poisson limit theorems - nonconventional sums - multiple recurrence
The Poisson limit theorem which appeared in 1837 seems to be the first law of rare events in probability. Various generalizations of it and estimates of errors of Poisson approximations were obtained in probability and more recently this became a popular topic in dynamics in the form of study of asymptotics of numbers of arrivals at small (shrinking) sets by a stochastic process or by a dynamical system. I will describe recent results on Poisson ...

60F05 ; 37D35 ; 37A50

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Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

We study law of rare events for random dynamical systems. We obtain an exponential law (with respect to the invariant measure of the skew-product) for super-polynomially mixing random dynamical systems.
For random subshifts of finite type, we analyze the distribution of hitting times with respect to the sample measures. We prove that with a superpolynomial decay of correlations one can get an exponential law for almost every point and with stronger mixing assumptions one can get a law of rare events depending on the extremal index for every point. (These are joint works with Benoit Saussol and Paulo Varandas, and Mike Todd).
We study law of rare events for random dynamical systems. We obtain an exponential law (with respect to the invariant measure of the skew-product) for super-polynomially mixing random dynamical systems.
For random subshifts of finite type, we analyze the distribution of hitting times with respect to the sample measures. We prove that with a superpolynomial decay of correlations one can get an exponential law for almost every point and with ...

37B20 ; 37A50 ; 37A25 ; 37Dxx

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- 394 p.
ISBN 978-0-521-68161-2

London mathematical society lecture note series , 0331

Localisation : Collection 1er étage

analyse numérique # complexité # fonction spéciale # polynôme orthogonal # géométrie algébrique # calculatoire # EDP # multirésolution d'EDP # modélisation géométrique # théorie de controle # intégration géométrique # mécanique calculatoire # théorie de l'apprentissage # optimisation # informatique # jeu algorithmique # traitement du signal # traitement de l'image # analyse formelle # matrice aléatoire # approximation # théorie des nombres calculatoire # dynamique calculatoire # calcul stochastique analyse numérique # complexité # fonction spéciale # polynôme orthogonal # géométrie algébrique # calculatoire # EDP # multirésolution d'EDP # modélisation géométrique # théorie de controle # intégration géométrique # mécanique calculatoire # théorie de l'apprentissage # optimisation # informatique # jeu algorithmique # traitement du signal # traitement de l'image # analyse formelle # matrice aléatoire # approximation # théorie des nombres ...

65-06

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