We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ϕj and study the nonparametric estimation of the density of the random effect ϕj in two kinds of mixed...

In this paper, we study the problem of the nonparametric estimation of the marginal density f of a class of continuous time processes. To this aim, we use a projection estimator and deal with the integrated mean square risk. Under Castellana and Leadbetter's condition (Stoch. Proc. Appl. 21...

In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step [Delta]. The asymptotic framework is: n tends to infinity, [Delta]=[Delta]n tends to zero while n[Delta]n tends to infinity. First, we use a...

In this paper, we study the problem of nonparametric estimation of the mean and variance functions b and [sigma]2 in a model: Xi+1=b(Xi)+[sigma](Xi)[var epsilon]i+1. For this purpose, we consider a collection of finite dimensional linear spaces. We estimate b using a mean squares estimator built...

Let (Vt) be a stationary and [beta]-mixing diffusion with unknown drift and diffusion coefficient. The integrated process is observed at discrete times with regular sampling interval . For both the drift function and the diffusion coefficient of the unobserved diffusion (Vt), we build...