Semi-stationary clearing processes

Large deviations for Gaussian stationary processes and semi-classical analysis

In this paper, we obtain a large deviation principle for quadratic forms of Gaussian stationary processes. It is established by the conjunction of a result of Roch and Silbermann on the spectrum of products of Toeplitz matrices together with the analysis of large deviations carried out by Gamboa, Rouault and the first author. An alternative proof of the needed result on Toeplitz matrices, based...

Stationary Processes

Stationary processes are stochastic processes whose probabilistic structure is unaffected by shifts in time. According to the interpretation of the term “probabilistic structure”, one distinguishes weak sense stationary processes, where only the covariance structure is supposed to be invariant, and strict sense stationary processes, for which all finitedimensional distributions have to remain t...

Stationary processes

Definition 1 (Time Series). A time series is a sequence of observations ordered with respect to a time index t, taking values in an index set S. If the set S contains a finite or countable number of elements we speak of discrete-time time series and the generic observation is indicated with the symbol yt, while if S is a continuum we have a continuous-time time series, whose generic observation...

On optimal stationary couplings between stationary processes

By a classical result of Gray et al. (1975) the %̄ distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge–Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings whi...

The KTH Visit in Semi-Markov Processes