Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a Hamilton-Jacobi equation with random Hamiltonian $H(p,x,\omega) = K(p) - V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/|\log \epsilon|)$. The proof relies on a modified Poincar\'e inequality of Talagrand

Invariant densities for dynamical systems with random switching

We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that H\"ormander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure.Comment: 16 pages; we replaced our original article to point out and close a gap in the discussion of the Lorenz system in Section 7 (see Remark 2); this gap is only present in the journal version of this article --- it wasn't present in the previous arxiv versio

Positive temperature versions of two theorems on first-passage percolation

The estimates on the fluctuations of first-passsage percolation due to Talagrand (a tail bound) and Benjamini--Kalai--Schramm (a sublinear variance bound) are transcribed into the positive-temperature setting of random Schroedinger operators.Comment: 15 pp; to appear in GAFA Seminar Note

Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

Learning in games with continuous action spaces and unknown payoff functions

International audienc

Facteurs prédictifs de la chute chez l'hémiplégique vasculaire en centre de médecine physique [Factors predicting falls by patients with vascular hemiplegia at a physical medicine center]

To determine factors predicting falls by patients with vascular hemiplegia to establish a program aimed at preventing falls in this population. A comparative prospective study performed over 19 months with 44 patients older than 16 years who had had a cerebral vascular accident (CVA, stroke) and were consequently admitted to the Centre Richelie. The exclusion criteria were represented by CVA history, evidence of another form of encephalic lesion, and subsequent admission to hospital after hemiplegia or for follow-up. Assessment consisted of taking note of the mechanism of the fall, possible lesions, and number of falls and analyzing follow-up after the return home. Also included for all patients was information on 20 variables that could be risk factors for fall. The patients' average age was 60.43+/-13.43 years and 20 had had at least one fall (mean 2.2), which allowed us to determine a "falling" group and a control group. Statistical analysis revealed the following factors considered to predict falls: large amount of time prior to hospitalization and lengthy hospitalization, low functional independence measure for entering and leaving, the existence of sensitivity disorders, spatial neglect, failed seated and standing equilibrium, and sedative treatment. In most cases, whatever their nature, falls occurred during transfers (68% of cases). Most often, the post-fall lesions were minor. However, in one case, a femur neck fracture necessitated osteosynthesis. One-third of the patients had a fall at home (as opposed to 5% of the control group). Our results confirm those in the literature. The predictive factors for falls in patients with hemiplegia are therefore well established and essentially correlate with the CVA. This consideration must lead to implementation of a prevention program including material-based as well as human measures

Un simple livret d'information peut contribuer à réduire l'incapacité fonctionnelle de patients lombalgiques subaigus et chroniques. Etude contrôlée randomisée en milieu de rééducation [The role of an information booklet or oral information about back pain in reducing disability and fear-avoidance beliefs among patients with subacute and chronic low back pain. A randomized controlled trial in a rehabilitation unit]

To compare the efficacy of an information booklet or oral information about back pain in reducing disability and fear-avoidance beliefs among patients with subacute and chronic low back pain referred to a rehabilitation department. An alternate-month design was used for 142 patients with subacute or chronic low back pain who were hospitalized for treatment. Seventy-two patients received written standardized information about back pain (the "back book") and usual physical therapy (intervention group), and 70 received usual physical therapy only along with nonstandardized oral information (control group). The main outcome measure was disability (measured on the Quebec back-pain disability scale), and secondary outcome measures were pain intensity (measured on a visual analog scale), fear-avoidance beliefs (measured on the Fear-Avoidance Beliefs Questionnaire [FABQ] Physical component), and knowledge of the relation of back pain to physical activity assessed at baseline, just before discharge from the hospital and 3 months after discharge. Satisfaction related to the information received was assessed on the day of discharge. Receiving the "back book" had a significant impact on disability at 3 months, from 48.40+/-14.55 to 34.57+/-18.42 in the intervention group and from 52.17+/-16.88 to 42.40+/-14.95 in the control group (p=0.03). Receipt of the book also had a significant impact on patients' knowledge and satisfaction about information but a nonsignificant effect on fear-avoidance beliefs. Providing an information booklet about back pain to patients with subacute and chronic low back pain referred to a rehabilitation unit contributes to reduced disability in these patients