Convergence en loi des H-variations d'un processus gaussien stationnaire sur R
Convergence in fractional models and applications.
Convergence rates for the full gaussian rough paths
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type...
Curvilinear integrals along enriched paths.
Degenerate limit laws for the maxima of trigonometric polynomials with random coefficients
Delay equations driven by rough paths.
Density formula and concentration inequalities with Malliavin calculus.
Des résultats nouveaux sur les processus gaussiens
Description de certains processus markoviens indexés par des sous-ensembles du cercle
Deux exemples d'utilisation de mesures majorantes
Die Anzahl der lokalen Maximalstellen eines stationären Gauszschen Prozesses.
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Distance de Fortet-Mourier et fonctions log-concaves
Distortion mismatch in the quantization of probability measures
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Distributions gaussiennes et temps locaux d'intersection
Efficient measurement of higher-order statistics of stochastic processes
This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance...
Einige Bemerkungen zu den Gauss-Verteilungen auf lokalkompakten Abelschen Gruppen.
Elliptic gaussian random processes.
We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol...
Enhanced Gaussian processes and applications
We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.
Entropy estimate for -monotone functions via small ball probability of integrated Brownian motions.