This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processe...

We propose non-stationary spectral kernels for Gaussian process regression. Wepropose to model the spectral density of a non-stationary kernel function as amixture of input-dependent Gaussian process frequency density surfaces. Wesolve the generalised Fourier transform with such a model, and present a familyof non-stationary and non-monotonic kernels that can learn input-depende...

Simulation models of real-life systems often assume stationary (homogeneous) Poisson arrivals. Therefore, when nonstationary arrival processes are required it is natural to assume Poisson arrivals with a time-varying arrival rate. For many systems, however, this provides an inaccurate representation of the arrival process which is either more or less variable than Poisson. In this paper we exte...

This paper offers a way to construct a locally optimal stationary approximation for a non-stationary Gaussian process. In cases where this construction leads to a unique stationary approximation we call it a stationary tangent. This is the case with Gaussian processes governed by smooth n-dimensional correlations. We associate these correlations with equivalence classes of curves in R. These ar...

We are interested in the functional convergence in distribution of the process of quadratic variations taken along a regular partition for a large class of Gaussian processes indexed by 0; 1], including the standard Wiener process as a particular case. This result is applied to the estimation of a time deformation that makes a non-stationary Gaussian process stationary.

The early cytokines production in response to live logarithmic and stationary phase promastigotes of Leishmania major was examined on the peripheral blood cells of the healthy individuals. Whole blood cultures were stimulated by either logarithmic or stationary phase promastigotes. IFN- and IL-10 productions were assessed by specific sandwich ELISA. The results showed that the logarithmic prom...

the early cytokines production in response to live logarithmic and stationary phase promastigotes of leishmania major was examined on the peripheral blood cells of the healthy individuals. whole blood cultures were stimulated by either logarithmic or stationary phase promastigotes. ifn- and il-10 productions were assessed by specific sandwich elisa. the results showed that the logarithmic prom...

Many time series in the applied sciences display a time-varying second order structure. In this article, we address the problem of how to forecast these non-stationary time series by means of non-decimated wavelets. We first consider a model in which only the variance evolves with time. We define a predictor for this model and show an application to the Dow Jones index. Then, we generalise the ...