Lévy processes form a wide and rich class of random process, and have many applications
ranging from physics to finance. Stochastic calculus is the mathematics of systems …

Transfer operators provide a rich framework for representing the dynamics of very general,
nonlinear dynamical systems. When interacting with reproducing kernel Hilbert spaces …

Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which:
X fulfils the ergodic theorem for any initial distribution; and X is exponentially β-mixing …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

We suppose that a Lévy process is observed at discrete time points. A rather general
construction of minimum-distance estimators is shown to give consistent estimators of the …

In this chapter we review stochastic modelling methods in climate science. First we provide a
conceptual framework for stochastic modelling of deterministic dynamical systems based on …

The chapters of this volume represent the revised versions of the main papers given at the
seventh Séminaire Européen de Statistique on “Statistics for Stochastic Differential …

Just as ARMA processes play a central role in the representation of stationary time series
with discrete time parameter,(Y_n) _ n ∈ Z (Y n) n∈ Z, CARMA processes play an …

In this paper, we study an algorithm (which we call the support reduction algorithm) that can
be used to compute non‐parametric M‐estimators in mixture models. The algorithm is …

In this article we propose a maximum likelihood methodology to estimate the parameters of
a one-dimensional stationary process of Ornstein-Uhlenbeck type that is constructed via a …