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...

Consider a one-dimensional diffusion with unknown positive drift and small variance [var epsilon]. We prove the asymptotic sufficiency of the complete or of some partial observations of the first hitting times process of the diffusion, as [var epsilon] goes to 0.

In this paper, we consider a stochastic volatility model ("Y"_"t", "V"_"t"), where the volatility (V_"t") is a positive stationary Markov process. We assume that ("ln""V"_"t") admits a stationary density "f" that we want to estimate. Only the price process "Y"_"t" is observed at "n" discrete times...

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...

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...

We consider a diffusion model of small variable type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model. In the sense of asymptotic equivalence of experiments, it is shown that observation of the diffusion process until...