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...

The method introduced by Leroux [Maximum likelihood estimation for hidden Markov models, Stochastic Process Appl. 40 (1992) 127-143] to study the exact likelihood of hidden Markov models is extended to the case where the state variable evolves in an open interval of the real line. Under rather...

Consider a compound Poisson process which is discretely observed with sampling interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Delta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">Δ</mi> </math> </EquationSource> </InlineEquation> until exactly <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>