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 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...

Abstract We consider a Lévy driven stochastic convolution, also called continuous time Lévy driven moving average model X(t)=\int_{0}^{t}a(t-s)\,dZ(s) , where 𝑍 is a Lévy martingale and the kernel a(\,{.}\,) a deterministic function square integrable on \mathbb{R}^{+} . Given 𝑁 i.i.d....

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...