Nonlinear structures determined by measures on Banach spaces
Non-negative linear processes
Conditions under which the linear process is non-negative are investigated in the paper. In the definition of the linear process a strict white noise is used. Explicit results are presented also for the models AR(1) and AR(2).
Nonparametric adaptive estimation for pure jump Lévy processes
This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at n discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive estimator....
Nonparametric estimation of the derivatives of the stationary density for stationary processes
In this article, our aim is to estimate the successive derivatives of the stationary density f of a strictly stationary and β-mixing process (Xt)t≥0. This process is observed at discrete times t = 0,Δ,...,nΔ. The sampling interval Δ can be fixed or small. We use a penalized least-square approach to compute adaptive estimators. If the derivative f(j)belongs to the Besov space B 2 , ∞ α , then our estimator converges at rate (nΔ)−α/(2α+2j+1). Then we consider a diffusion with known diffusion coefficient....
Nonparametric inference for discretely sampled Lévy processes
Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.
Non-perturbative approach to random walk in Markovian environment.
Non-polar points for reflected brownian motion
Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
Norm convergence of random walks on compact hypergroups.
Norm convergent expansion for -valued Gaussian random elements
Normal covariances
Normal martingales and polynomial families
Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve...
Note on approximate non-Gaussian filtering with nonlinear observation relation
Note on nonlinear semigroups and free boundary problem for controlled Markov processes
Note on the central limit theorem for stationary processes
Note on the maximal spectral type of a stochastic process.
Note on the selection properties of set-valued semimartingales
Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
Note sur les processus d'Ornstein-Uhlenbeck
Note sur l'exposé précédent
Notes on dependence with complete connections