Ergodic BSDEs with Multiplicative and Degenerate Noise

In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type we can give a stochastic representation of a large class of Ergodic HJB equations; morever our general results can be applied to get the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs

Stochastic Maximum Principle for optimal advertising models with delay and non-convex control space

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation

Singular Limit of BSDEs and Optimal Control of two Scale Stochastic Systems in Infinite Dimensional Spaces

In this paper we study by probabilistic techniques the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is represented as the solution of a backward stochastic differential equation (BSDE) that it is shown to converge towards a reduced BSDE. The noise is assumed to be additive both in the slow and the fast equations for the state. Some non degeneracy condition on the slow equation is required. The limit BSDE involves the solution of an ergodic BSDE and is itself interpreted as the value function of an auxiliary stochastic control problem on a reduced state space

Linear-quadratic optimal control under non-Markovian switching

We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism is not required to be Markovian. The problem is solved by means of a Riccati equation, which a backward stochastic differential equation driven by the Brownian motion and by the random measure associated to the marked point process

Communication and visiting policies in Italian intensive care units during the first COVID-19 pandemic wave and lockdown: a nationwide survey

Background: During the first coronavirus disease 2019 (COVID-19) pandemic wave, an unprecedented number of patients with respiratory failure due to a new, highly contagious virus needed hospitalization and intensive care unit (ICU) admission. The aim of the present study was to describe the communication and visiting policies of Italian intensive care units (ICUs) during the first COVID-19 pandemic wave and national lockdown and compare these data with prepandemic conditions. Methods: A national web-based survey was conducted among 290 Italian hospitals. Each ICU (active between February 24 and May 31, 2020) was encouraged to complete an individual questionnaire inquiring the hospital/ICU structure/organization, communication/visiting habits and the role of clinical psychology prior to, and during the first COVID-19 pandemic wave. Results: Two hundred and nine ICUs from 154 hospitals (53% of the contacted hospitals) completed the survey (202 adult and 7 pediatric ICUs). Among adult ICUs, 60% were dedicated to COVID-19 patients, 21% were dedicated to patients without COVID-19 and 19% were dedicated to both categories (Mixed). A total of 11,102 adult patients were admitted to the participating ICUs during the study period and only approximately 6% of patients received at least one visit. Communication with family members was guaranteed daily through an increased use of electronic devices and was preferentially addressed to the same family member. Compared to the prepandemic period, clinical psychologists supported physicians more often regarding communication with family members. Fewer patients received at least one visit from family members in COVID and mixed-ICUs than in non-COVID ICUs, l (0 [0–6]%, 0 [0–4]% and 11 [2–25]%, respectively, p < 0.001). Habits of pediatric ICUs were less affected by the pandemic. Conclusions: Visiting policies of Italian ICUs dedicated to adult patients were markedly altered during the first COVID-19 wave. Remote communication was widely adopted as a surrogate for family meetings. New strategies to favor a family-centered approach during the current and future pandemics are warranted