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....

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...