ECONOMIC AND FINANCIAL CRISIS IMPACT ON RAIL SECTOR

Among transport modes existing today, rail remains of great interest because of certain benefits arising from that is the least polluting and most environmentally friendly. These are just some of the reasons why, in recent years, the European Union's strategy is trying to develop and implement programs to revive rail transport in the Community and to draw more traffic to this type of transport. Economic and financial crisis that has put imprint on the sector and the economy. The paper proposes a brief analysis of the development of rail passengers and freight in the Union Europe in period 2006-2009. As a transport sector with less risk factor than other types of transport, the paper presents a risk profile of railways.rail, risks in rail transport, effects of the crisis in rail transport

A strong invariance principle for associated random fields

In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n\to \infty. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multi-parameter blocking technique, the Csorgo and Revesz [Z. Wahrsch. Verw. Gebiete 31 (1975) 255-260] quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995) 136-144] rate of convergence in the CLT.Comment: Published at http://dx.doi.org/10.1214/009117904000001071 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Linear SPDEs with harmonizable noise

Using tools from the theory of random fields with stationary increments, we introduce a new class of processes which can be used as a model for the noise perturbing an SPDE. This type of noise (called harmonizable) is not necessarily Gaussian, but it includes the spatially homogeneous Gaussian noise introduced in Dalang (1999), and the fractional noise considered in Balan and Tudor (2010). We derive some general conditions for the existence of a random field solution of a linear SPDE with harmonizable noise, under some mild conditions imposed on the Green function of the differential operator which appears in this equation. This methodology is applied to the study of the heat and wave equations (possibly replacing the Laplacian by one of its fractional powers), extending in this manner the results of Balan and Tudor (2010) to the case $H<1/2$.Comment: 31 page