Persistence of some additive functionals of Sinai's walk

We are interested in Sinai's walk $(S\_n)\_{n\in\mathbb{N}}$. We prove that the annealed probability that $\sum\_{k=0}^n f(S\_k)$ is strictly positive for all $n\in[1,N]$ is equal to $1/(\log N)^{\frac{3-\sqrt{5}}{2}+o(1)}$, for a large class of functions $f$, and in particular for $f(x)=x$. The persistence exponent $\frac{3-\sqrt{5}}{2}$ first appears in a non-rigorous paper of Le Doussal, Monthus and Fischer, with motivations coming from physics. The proof relies on techniques of localization for Sinai's walk and uses results of Cheliotis about the sign changes of the bottom of valleys of a two-sided Brownian motion.Comment: 30 pages, 2 figure

Some properties of the rate function of quenched large deviations for random walk in random environment

In this paper, we are interested in some questions of Greven and den Hollander about the rate function $I\_{\eta}^q$ of quenched large deviations for random walk in random environment. By studying the hitting times of RWRE, we prove that in the recurrent case, $\lim\_{\theta\to 0^+}(I\_{\eta}^q)''(\theta)=+\infty$, which gives an affirmative answer to a conjecture of Greven and den Hollander. We also establish a comparison result between the rate function of quenched large deviations for a diffusion in a drifted Brownian potential, and the rate function for a drifted Brownian motion with the same speed

Random walk in random environment in a two-dimensional stratified medium with orientations

We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed orientations under general hypotheses. This contrasts with the model of Campanino and Petritis, in which probabilities to stay on these lines are all equal. We also establish a result of convergence in distribution for this walk with suitable normalizations under more precise assumptions. In particular, our model proves to be, in many cases, even more superdiffusive than the random walks introduced by Campanino and Petritis.Comment: 23 pages, 1 figur

Renewal structure and local time for diffusions in random environment

We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W\_\kappa$, with 0\textless{}\kappa\textless{}1, and focus on the behavior of the local times $(\mathcal{L}(t,x),x)$ of $X$ before time t\textgreater{}0.In particular we characterize the limit law of the supremum of the local time, as well as the position of the favorite sites. These limits can be written explicitly from a two dimensional stable L{\'e}vy process. Our analysis is based on the study of an extension of the renewal structure which is deeply involved in the asymptotic behavior of $X$.Comment: 61 page

An Inflation Forecasting Model for the Euro Area.

With the European economic integration, the understanding of inflation and inflationary pressures requires to analyse both the national level and the whole Euro area level. This is true in particular for the inflation forecasts that are carried out within the Eurosystem and published four times a year in the ECB Monthly Bulletin. For that purpose, the Banque de France is currently building tools for the Euro area in addition to those already in use for France. The present study puts forward a simple model of short-term developments (one year ahead) in inflation, as measured by the Harmonized Index of Consumer Prices (HICP) of the Euro area. This model does not take into account the feed-back effect of prices on activity, which should be considered in order to analyse medium-term price developments. It could hence be improved along these lines in the future. The model includes seven equations, explaining the total HICP of the Euro area and some of its sector-based sub-indexes (services, manufacturing sector, unprocessed food, processed food, energy and underlying inflation, defined as HICP inflation excluding unprocessed food and energy prices). It uses exogenous variables such as unit labour cost, import deflator, indicators of tightening in the labour market, or in the goods market, and indirect tax indicators. We have favoured an empirical approach rather than a strict compliance with theoretical models, paying particularly attention to the fit of the equations to the data. However, this model is able to provide relevant economic interpretations of recent price developments. Finally, we assess the forecasting performance of the model in traditional in-sample and out-of-sample rolling event evaluations. To do so, the forecasts were compared to the ones obtained from simple autoregressive equations, which are also commonly used to forecast short-term price developments. On the whole, the model provides more accurate forecasts than those provided by the autoregressive model, and a sector-based disaggregated approach outperforms a single equation to forecast total HICP. Part of this result may come from dummy variables that correspond to well identified shocks that improve both the econometric characteristics and forecast performance of the equations of our model.Inflation ; Economic Modelling ; Forecast.