This paper proposes a general approach to obtain asymptotic lower bounds for the estimation of random functionals. The main result is an abstract convolution theorem in a non parametric setting,â€¦ (More)

We consider a multidimensional diffusion X with drift coefficient b(Xt, Î±) and diffusion coefficient Îµa(Xt, Î²) where Î± and Î² are two unknown parameters, while Îµ is known. For a high-frequency sampleâ€¦ (More)

Multifractal analysis of multiplicative random cascades is revisited within the framework of mixed asymptotics. In this new framework, the observed process can be modeled by a concatenation ofâ€¦ (More)

In this paper, we prove some limit theorems for the Fourier estimator of multivariate volatility proposed by Malliavin and Mancino ( [14], [15]). In a general framework of discrete time observationsâ€¦ (More)

We study the parametric problem of estimating the drift coefficient in a stochastic volatility model Yt = âˆ« t 0 âˆš Vs dWs , where Y is a log price process and V the volatility process. Assuming thatâ€¦ (More)

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X . Our data are given by âˆ« 1 0 Xâ€¦ (More)

In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe theâ€¦ (More)

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a di usion process X. Our data are given by âˆ« 1 0 Xâ€¦ (More)

We study the problem of the optimal estimation of the jumps for stochastic processes. We assume that the stochastic process (Xt)tâˆˆ[0,1] is discretely observed with a sampling step of size 1/n. Weâ€¦ (More)