Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.

Clinical utility of exercise training in chronic systolic heart failure

The volume of literature attesting to the clinical benefits of exercise training in patients with stable chronic heart failure (CHF) is substantial. Training can improve symptoms and exercise capacity, as well as reducing morbidity, mortality, and rates of emergency hospitalization. These benefits are apparent in all patients with stable CHF, irrespective of age or sex, or the etiology or severity of heart failure. Training regimens for patients with stable, systolic CHF should form part of a comprehensive heart-failure support effort and are best delivered using supervised in-hospital exercise combined with some training at home or in a group setting in community centers. In this Review, the modes and intensity of exercise training, selection of patients, duration of training effects, and other clinical guidance for using this treatment option are discussed