Cauchy's principal value of local times of Lévy processes with no negative jumps via continuous branching processes.
Chaotic behavior of infinitely divisible processes
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Characterizations of processes with stationary and independent increments under -expectation
Our purpose is to investigate properties for processes with stationary and independent increments under -expectation. As applications, we prove the martingale characterization of -Brownian motion and present a pathwise decomposition theorem for generalized -Brownian motion.
Classes uniformes de processus gaussiens stationnaires
Comparison between criteria leading to the weak invariance principle
The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28...
Competing particle systems and the Ghirlanda-Guerra identities.
Conditions d'isomorphisme des flots spéciaux
Construction of a class of stationary processes with applications in reliability
Corrigendum to the paper: “A remark on the weighted averages for superadditive processes”.
Covariance structure of wide-sense Markov processes of order k ≥ 1
A notion of a wide-sense Markov process of order k ≥ 1, , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of is the k-dimensional process . The covariance structure of is considered in the general case and in the periodic case. In the general case it is shown that iff is a k-dimensional WM(1) process and iff the covariance function of has the triangular property....