Caractérisation de processus à trajectoires majorées ou continues
Central and non-central limit theorems for weighted power variations of fractional brownian motion
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral...
Central limit theorem for solutions of random initialized differential equations: a simple proof.
Characterization of equilibrium measures for critical reversible Nearest Particle Systems
We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than and obeys some natural regularity conditions.
Classes uniformes de processus gaussiens stationnaires
CLT for linear spectral statistics of Wigner matrices.
Comparaison de mesures gaussiennes et de mesures produit
Comparaison de tests d'hypothèses pour des processus gaussiens
Comparison theorems for small deviations of random series.
Concentration of measure and isoperimetric inequalities in product spaces
Continuity of stochastic convolutions
Let be a Brownian motion, and let be the space of all continuous periodic functions with period 1. It is shown that the set of all such that the stochastic convolution , does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.
Continuous factorizations of covariance operators and Gaussian processes
Control of a Gaussian process by rarefying its innovation process.
Convergence and convergence rate to fractional Brownian motion for weighted random sums.
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.