We consider the Cauchy problem for Klein–Gordon equation in $${\mathbb{R}}^{d},d\ge 1,$$ with random initial data. introduce a family of measures $${\mu }_{0}^{\varepsilon },\varepsilon >0$$ depending on small parameter ε. The }$$ are assumed to be locally homogeneous or slowly varying under spatial shifts order o(ε−1) and inhomogeneous ε−1. Moreover, correlation functions decrease uniformly ε ...

Abstract We consider point-to-point last-passage times to every vertex in a neighbourhood of size $$\delta N^{\nicefrac {2}{3}}$$ ? N 2 3 at distance N from the starting point. The increme...

Abstract Machine learning algorithms have been increasingly applied to spatial numerical modeling. However, it is important understand when such methods will underperform. are impacted by dataset shift ; modeling domains of interest present non-stationarities there no guarantee that the trained models effective in unsampled areas. This work aims compare stationarity requirement geostatistical c...

This paper applies conventional panel unit root tests and panel stationarity tests with and without structural breaks to examine the time series properties of real Gross Domestic Product (GDP) per capita for a panel of eight Pacific Island economies. The panel unit root and panel stationarity tests without structural breaks suggest that for the panel as a whole real GDP per capita contains a un...

Blind separation of independent sources can be achieved by exploiting non Gaussianity, non stationarity or time correlation. This paper examines in a unified framework the objective functions associated to these three routes to source separation. They are the ‘easy routes’ in the sense that the underlying models are the simplest models able to capture the statistical structures which make sourc...

Many time series are not second-order stationary and it is not appropriate to analyze them using methods designed for stationary series. This article introduces a new test for second-order stationarity that detects different kinds of departures from stationarity than those based on Fourier methods. The new test is also computationally fast, designed to work with Gaussian and a wide range of non...

In this paper, we show that the central limit theorem (CLT) satisfied by the data-driven Multidimensional Increment Ratio (MIR) estimator of the memory parameter d established in Bardet and Dola (2012) for d ∈ (−0.5, 0.5) can be extended to a semiparametric class of Gaussian fractionally integrated processes with memory parameter d ∈ (−0.5, 1.25). Since the asymptotic variance of this CLT can b...

For nonstationary time series the fixed Fourier basis is no longer canonical. This article shows how the choice of analysis basis influences the detection of nonstationarities within time series. Rather than limit our basis choice to wavelet or Fourier functions we develop a new stationarity test using a (multiple) bootstrap hypothesis test based on non-decimated wavelet packets. Non-decimated ...

This paper aims at developing effective numerical methods for solving mathematical programs with equilibrium constraints. Due to the existence of complementarity constraints, the usual constraint qualifications do not hold at any feasible point, and there are various stationarity concepts such as Clarke, Mordukhovich, and strong stationarities that are specially defined for mathematical program...