is not a semimartingale
inequalities for functionals of brownian motion
La propriété de représentation prévisible dans la filtration naturelle d'un ensemble régénératif
Large and moderate deviations for the local time of a recurrent Markov chain on
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...
Large deviations for local times of stable processes and stable random walks in 1 dimension.
Large favourite sites of simple random walk and the Wiener process.
Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables
Le drap brownien comme limite en loi des temps locaux linéaires
Le mouvement brownien de Lévy indexé par comme limite centrale de temps locaux d’intersection
Le problème de Skorokhod sur : une approche avec le temps local
Le support exact du temps local d'une martingale continue
Les changements de temps en théorie générale des processus
Les travaux d'Azéma sur le retournement du temps
Lévy classes and self-normalization.
Limit theorems and variation properties for fractional derivatives of the local time of a stable process
Limit theorems for some functionals with heavy tails of a discrete time Markov chain
Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain (Xn,n ≥ 0) with invariant distribution μ. We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable functionf. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then use existing results of convergence...
Limit theorems for stationary Markov processes with L2-spectral gap
Let be a discrete or continuous-time Markov process with state space where is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. is assumed to be a Markov additive process. In particular, this implies that the first component is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process is shown to satisfy the...
Linear modulus of a multidimensional semigroup of -contractions and a differentiation theorem
Local behaviour of local times of super-brownian motion