Asymptotics of weighted empirical processes of linear fields with long-range dependence
Burkholder's inequality for multiindex martingales.
Capacity and energy for multiparameter Markov processes
Capacity estimates, boundary crossings and the Ornstein-Uhlenbeck process in Wiener space.
Caractérisation des martingales à deux paramètres indépendantes du chemin
Chaos expansions and local times.
In this note we prove that the Local Time at zero for a multiparametric Wiener process belongs to the Sobolev space Dk - 1/2 - ε,2 for any ε > 0. We do this computing its Wiener chaos expansion. We see also that this expansion converges almost surely. Finally, using the same technique we prove similar results for a renormalized Local Time for the autointersections of a planar Brownian motion.
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.
Classe et martingales fortes à paramètre bidimensionnel
Computing the expectation of the Azéma-Yor stopping times
Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels
Correction : «Temps local pour les martingales à deux indices par rapport à sa variation quadratique»
Detection of transient change in mean – a linear behavior inside epidemic interval
A procedure for testing occurrance of a transient change in mean of a sequence is suggested where inside an epidemic interval the mean is a linear function of time points. Asymptotic behavior of considered trimmed maximum-type test statistics is presented. Approximate critical values are obtained using an approximation of exceedance probabilities over a high level by Gaussian fields with a locally stationary structure.
Different approaches to stochastic parabolic differential equations
Différents types de variations-produit pour une semi-martingale représentable à deux paramètres
Nous étendons les notions de processus croissants associés à un processus au cas des processus à paramètre bidimensionnel : existence et égalité de limites de sommes de carrés d’accroissements (conditionnés ou non) sur des rectangles, sur des segments parallèles, ou mixtes.
Directionally convex ordering in multidimensional jump diffusions models.
Divergences of Gauss-Markov random fields with application to statistical inference
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...
Ergodic behaviour of “signed voter models”
We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat.41(2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site and a site is negative (respectively positive) the site will contribute towards the flip rate of if and only if the two current spin values are equal (respectively opposed)....
Ergodicity of PCA: equivalence between spatial and temporal mixing conditions.
Estimates of the Hausdorff dimension of the boundary of positive brownian sheet components