Limit theorems and applications (SAMSOS, 2008)

Episodes

1. 1

   01 - Estimating the Degree of Activity of jumps in High Frequency Data - Jean JACOD

   Jean Jacod. Université Paris6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1265816883468 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 51 mn

   Jan 13, 2008

   50m
2. 2

   02 - Rates of convergence for minimal distances in the central limit theorem under projective criteria - Emmanuel RIO

   In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear...

   Jan 12, 2008

   43m
3. 3

   03 - Stein's method and weak convergence on Wiener space - Giovanni PECCATI

   We will show taht one can combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of arbitrary regular functionals of a given Gaussian field (here, the notion of regularity is in the sense of Malliavin derivability). When applied...

   Jan 11, 2008

   41m
4. 4

   04 - Asymptotic results for empirical measures of weighted sums of independant random variables- Bernard BERCU

   We investigate the asymptotic behavior of a particular family of weighted sums of independent standardized random variables with uniformly bounded third moments. We prove that the empirical CDF of the resulting partial sums converges almost surely to the normal CDF. It allows us to deduce the...

   Jan 10, 2008

   35m
5. 5

   05 - Group Representations and High-Resolution Central Limit Theorems for Subordinated Spherical Random Fields - Domenico MARINUCCI

   We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we establish a new connection with random walks on the the dual...

   Jan 9, 2008

   56m
6. 6

   06 - Weighted power variations of fractional and iterated Brownian motions - Ivan NOURDIN

   Ivan NOURDIN. Université Paris 6. Ecouter l'intervention : Bande son disponible au format mp3 Durée : 47 mn

   Jan 8, 2008

   46m
7. 1

   01 - Inverse problems for regular variation, linear filters, functional equations and a cancellation property for $\sigma$-finite measures - Gennady SAMORODNITSKY

   We study a group of related problems: the extent to which presence of regular variation of the tail of certain $sigma$-finite measures at the output of a linear filter determines the corresponding regular variation of a measure at the input to the filter. This turns out to be related to presence…

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   Jan 6, 2008

   46m
8. 7

   07 - On the existence of some ARCH($\infty$) processes - Philippe SOULIER

   Philippe SOULIER Université Paris 10 Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750174352 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 33 mn

   Jan 6, 2008

   32m
9. 2

   02 - An estimator for the quadratic variation of mixed Brownian fractional - Esko VALKEILA

   In the work (Bender, T. Sottinen, and E. Valkeila (2006)) we show that it is possible to extend the classical Black & Scholes hedging for a class of models, where the quadratic variation is identical to the Black & Scholes model. Dzhaparidze and Spreij show in (K. Dzhaparidze, and P. Spreij...

   Jan 5, 2008

   40m
10. 3

    03 - Central limit theorem for sampled sums of dependent random variables - Clémentine PRIEUR

    We prove a central limit theorem for linear triangular arrays under weak dependence conditions [1,3,4]. Our result is then applied to the study of dependent random variables sampled by a $Z$-valued transient random walk. This extends the results obtained by Guillotin-Plantard & Schneider [2]. An...

    Jan 4, 2008

    32m
11. 4

    04 - Lévy-stable behavior of squares - Donatas SURGAILIS

    We introduce a new modification of Sentana's (1995) Quadratic ARCH (QARCH), the Linear ARCH (LARCH) (Giraitis et al., 2000, 2004) and the bilinear models (Giraitis and Surgailis, 2002), which can combine the following properties: (a.1) conditional heteroskedasticity (a.2) long memory (a.3) the...

    Jan 3, 2008

    36m
12. 5

    05 - Weak dependence, Models and Some Applications - Paul DOUKHAN

    Jan 2, 2008

    49m
13. 6

    06 - Multifractional random walk as fractional integral - Laure COUTIN

    Nous définissons une classe de processus multifractaux en intégrant une cascades multiplicative stationnaire contre un mouvement brownien fractionnaire. Les propriétés de scaling sont étudiées ainsi que le formalisme multifractal associé. This talk is based on a joint work with P.Abry, P.Chainais...

    Jan 1, 2008

    45m
14. 8

    08 - Contraction rates of posteriors based on Gaussian - Harry VAN ZANTEN

    Contraction rates of posterior distributions on nonparametric models are derived for Gaussian process priors. We show that the convergence rate depends on the small ball probabilities of the Gaussian process and on the position of the true parameter relative to the reproducing kernel Hilbert…

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    Dec 30, 2007

    33m
15. 1

    01 - Approximations and limit theory for quadratic forms of linear processes - Liudas GIRAITIS

    The paper develops a limit theory for the quadratic form $Q_{n,X}$ in linear random variables $X_1, ldots, X_n$ which can be used to derive the asymptotic normality of various semiparametric, kernel, window and other estimators converging at a rate which is not necessarily $n^{1/2}$. The theory...

    Dec 29, 2007

    50m
16. 2

    02 - Numerical scheme for RBSDE - Soledad TORRES

    We propose a method for numerical approximation of Reflected Backward Stochastic Differential Equations. Is based in the approximation for the Brownian motion by a simple random walk. We prove a weak convergence. This talk is based on joint work with Miguel Martinez and Jaime San Martin. Soledad...

    Dec 28, 2007

    43m
17. 3

    03 - Self-similar random fields and rescaled random balls models - Hermine BIERME

    We study generalized random fields which arise as rescaling limits of spatial configurations of uniformly scattered random balls as the mean radius of the balls tends to $0$ or infinity. Assuming that the radius distribution has a power law behavior, we prove that the centered and renormalized...

    Dec 27, 2007

    40m
18. 4

    04 - Local continuity - Tommi SOTTINEN

    We propose the concept of Local Continuity that is somewhat related to directional continuity. DEFINITION: Let X and Y be, say, metric spaces. A function f from X to Y is locally continuous at point x in X if one can find an open set U(x) such that (i) x belongs to the closure of U(x), (ii) if…

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    Dec 26, 2007

    48m
19. 5

    05 - Asymptotics for posterior hazards - Igor PRUNSTER

    A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. A comprehensive analysis of the asymptotic behaviour of such models is provided. Consistency of the posterior distribution is investigated and...

    Dec 25, 2007

    45m
20. 6

    06 - Invariance principle, multifractional Gaussian processes and long-range dependence - Renaud MARTY

    We establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity, of this process are studied. Moreover the limit process is compared...

    Dec 24, 2007

    31m