Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions

We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the $d$-dimensional torus with singular $p$-Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and Gaussian gradient Stratonovich noise with divergence-free coefficients. Assuming a weak defective commutator bound and a curvature-dimension condition, the well-posedness result is obtained in a stochastic variational inequality setup by using resolvent and Dirichlet form methods and an approximative It\^{o}-formula.Comment: 26 pages, 58 references. Essential changes to Version 4: Examples revised. Accepted for publication in Stochastic Processes and their Application

Implicit renewal theory for exponential functionals of L\'evy processes

We establish a new functional relation for the probability density function of the exponential functional of a L\'evy process, which allows to significantly simplify the techniques commonly used in the study of these random variables and hence provide quick proofs of known results, derive new results, as well as sharpening known estimates for the distribution. We apply this formula to provide another look to the Wiener-Hopf type factorisation for exponential functionals obtained in a series of papers by Pardo, Patie and Savov, derive new identities in law, and to describe the behaviour of the tail distribution at infinity and of the distribution at zero in a rather large set of situations

Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts

In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].Comment: http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2308&layout=abstrac

Technology shocks and the business cycle

Technology ; Business cycles

Novel Method to Process Cystic Fibrosis Sputum for Determination of Oxidative State

Background: Induced sputum is the most commonly used method to analyze airway inflammation in cystic fibrosis (CF) patients ex vivo. Due to the complex matrix of the sample material, precise and reliable analysis of sputum constituents depends critically on preanalytical issues. Objectives: Here we compared the commonly used method for sputum processing by dithiothreitol (DTT) with a novel mechanical method in regard to basal cellular parameters, neutrophil markers and glutathione (GSH) levels. Methods: Sputum samples from CF patients were processed in parallel with or without the use of DTT. The key improvement of the mechanical method was the processing in many very small aliquots. Cellular and humoral markers were assessed and compared according to Bland-Altman. Results: Total cell count, cell viability, differential cell count, neutrophil elastase levels and flow cytometrically analyzed neutrophil markers (CD63, CD11b, DHR) did not differ between the two methods. Intracellular and extracellular GSH levels were significantly higher in DTT-treated samples (p = 0.002). Conclusion: The mechanical sputum-processing method presented had a similar yield of cells and fluids as the conventional DTT method and the advantage of omitting the introduction of reducing agents. This method allows a more reliable analysis of redox-dependent airway inflammation in sputum cells and fluid from CF patients than methods utilizing DTT. Copyright (C) 2009 S. Karger AG, Base

Copayments for Ambulatory Care in Germany: A Natural Experiment Using a Difference-in-Difference Approach

In response to increasing health expenditures and a high number of physician visits, the German government introduced a copayment for ambulatory care in 2004 for individuals with statutory health insurance (SHI). Because persons with private insurance were exempt from the copayments, this health care reform can be regarded as a natural experiment. We used a difference-in-difference approach to examine whether the new copayment effectively reduced the overall demand for physician visits and to explore whether it acted as a deterrent to vulnerable groups, such as those with low income or chronic conditions. We found that there was no significant reduction in the number of physician visits among SHI members compared to our control group. At the same time, we did not observe a deterrent effect among vulnerable individuals. Thus, the copayment has failed to reduce the demand for physician visits. It is likely that this result is due to the design of the copayment scheme, as the copayment is low and is paid only for the first physician visit per quarter.copayments, ambulatory care, difference-in-difference, count data, zero-inflated-model