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...

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...