Consider some multivariate diffusion process X=(X t) t≥ 0 with unique invariant probability
measure and associated invariant density ρ, and assume that a continuous record of …

We consider nonparametric estimation of the transition operator P of a Markov chain and its
transition density p where the singular values of P are assumed to decay exponentially fast …

We introduce a new approach for estimating the invariant density of a multidimensional
diffusion when dealing with high-frequency observations blurred by independent noises. We …

The estimation of the diffusion matrix Σ of a high-dimensional, possibly time-changed Lévy
process is studied, based on discrete observations of the process with a fixed distance. A …

The nonparametric volatility estimation problem of a scalar diffusion process observed at
equidistant time points is addressed. Using the spectral representation of the volatility in …

As a starting point we prove a functional central limit theorem for estimators of the invariant
measure of a geometrically ergodic Harris-recurrent Markov chain in a multi-scale space …

This thesis deals with the long-time behavior of stochastic Fokker-Planck equations with
additive common noise and presents statistical methods for estimating the invariant measure …

Let X be a continuous-time strongly mixing or weakly dependent process and let T be a
renewal process independent of X. We show general conditions under which the sampled …

In this thesis, we consider the problem of nonparametric estimation of the diffusion
coefficients of a scalar time-homogeneous Itô diffusion process from discrete observations …

Matrix models are ubiquitous in modern statistics. For instance, they are used in finance to
assess interdependence of assets, in genomics to impute missing data and in movie …