Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Smoluchowski-Kramers approximation in the case of variable friction

We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered.Comment: already publishe

Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence takes place in the topology induced by a weighted variation norm and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

Prescriptive adherence to GINA guidelines and asthma control: An Italian cross sectional study in general practice

Background: Although general practitioners (GPs) are frequently the first healthcare professionals whom asthma patients refer to for their symptoms, few studies have explored the extent of adherence to guidelines for asthma management based on data provided directly by GPs. Aims of the present study were to assess drug prescriptions for asthma by GPs and to evaluate prescriptive adherence to GINA guidelines (GL) and its relationship with disease control in real life. Methods: 995 asthmatic patients (45% males, mean age 43.3 ± 17.7 yrs) were enrolled by 107 Italian GPs distributed throughout the country. Data on diagnosis, disease severity, prescribed anti-asthmatic drugs and control were collected through questionnaires filled out by GPs taking into consideration the 2009 GINA Guidelines. Data on drug use and chronic sinusitis, nasal polyposis, chronic bronchitis, emphysema were reported by patients through a self-administered questionnaire. Results: The large majority of patients were classified by GPs as having intermittent (48.4%) or mild persistent asthma (25.3%); 61% had co-morbid allergic rhinitis (AR). The prevalent therapeutic regimen used by patients was a combination of inhaled corticosteroids (ICS) plus long-acting β2-agonists (LABA) (54.1%), even in the intermittent/mild persistent group. ICS as mono-therapy or in combination with other drugs but LABA, was the second most frequently adopted treatment (14.4%). In general, the GPs adherence to GL treatment indications was 28.8%, with a significant association with a good asthma control (OR 1.85, 95% CI 1.18–2.92). On the other hand, comorbidity (OR 0.52, 95% CI 0.32–0.84), moderate (0.44, 0.28–0.69) and severe (0.06, 0.02–0.20) persistent asthma showed significant negative effects on asthma control. Conclusions: Our results show that over-treatment of intermittent/mild persistent asthma is frequent in the GPs setting while therapeutic regimens are more appropriately applied for moderate/severe asthma. In general, we found low adherence to GINA GL treatment recommendations even if its relevance in asthma control was confirmed

Bismut-Elworthy-Li formulae for Bessel processes

In this article we are interested in the differentiability property of the Markovian semi-group corresponding to the Bessel processes of nonnegative dimension. More precisely, for all δ ≥ 0 and T > 0, we compute the derivative of the function x↦PδTF(x), where (Pδt)t≥0 is the transition semi-group associated to the δ-dimensional Bessel process, and F is any bounded Borel function on R+. The obtained expression shows a nice interplay between the transition semi-groups of the δ—and the (δ + 2)-dimensional Bessel processes. As a consequence, we deduce that the Bessel processes satisfy the strong Feller property, with a continuity modulus which is independent of the dimension. Moreover, we provide a probabilistic interpretation of this expression as a Bismut-Elworthy-Li formula

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti

Electronic cigarette use in 12 European countries. Results from the TackSHS survey.

BACKGROUND: Limited data on electronic cigarette prevalence, patterns and settings of use are available from several European countries. METHODS: Within the TackSHS project, a face-to-face survey was conducted in 2017-2018 in 12 European countries (Bulgaria, England, France, Germany, Greece, Ireland, Italy, Latvia, Poland, Portugal, Romania and Spain). Overall, 11,876 participants, representative of the population aged ≥15 years in each country, provided information on electronic cigarette. RESULTS: 2.4% (95% confidence interval, CI: 2.2-2.7) of the subjects (2.5% among men and 2.4% among women; 0.4% among never, 4.4% among current- and 6.5% among ex-smokers) reported current use of electronic cigarette, ranging from 0.6% in Spain to 7.2% in England. Of the 272 electronic cigarette users, 52.6% were dual users (i.e., users of both electronic and conventional cigarettes) and 58.8% used liquids with nicotine. In all, 65.1% reported using electronic cigarette in at least one indoor setting where smoking is forbidden, in particular in workplaces (34.9%), and bars and restaurants (41.5%). Multivariable logistic regression analysis showed that electronic cigarette use was lower among older individuals (p for trend <0.001) and higher among individuals with high level of education (p for trend 0.040). Participants from countries with higher tobacco cigarette prices more frequently reported electronic cigarette use (odds ratio 3.62; 95% CI: 1.80-7.30). CONCLUSIONS: Considering the whole adult population of these 12 European countries, more than 8.3 million people use electronic cigarettes. The majority of users also smoked conventional cigarettes, used electronic cigarettes with nicotine and consumed electronic cigarettes in smoke-free indoor areas

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation