Backward SDEs for optimal control of partially observed path-dependent stochastic systems : A control randomization approach

We introduce a suitable backward stochastic differential equation (BSDE) to represent the value of an optimal control problem with partial observation for a controlled stochastic equation driven by Brownian motion. Our model is general enough to include cases with latent factors in Mathematical finance. By a standard reformulation based on the reference probability method, it also includes the classical model where the observation process is affected by a Brownian motion (even in presence of a correlated noise), a case where a BSDE representation of the value was not available so far. This approach based on BSDEs allows for greater generality beyond the Markovian case, in particular our model may include path-dependence in the coefficients (both with respect to the state and the control), and does not require any nondegeneracy condition on the controlled equation. We use a randomization method, previously adopted only for cases of full observation, and consisting in a first step, in replacing the control by an exogenous process independent of the driving noise and in formulating an auxiliary (\u201crandomized\u201d) control problem where optimization is performed over changes of equivalent probability measures affecting the characteristics of the exogenous process. Our first main result is to prove the equivalence between the original partially observed control problem and the randomized problem. In a second step, we prove that the latter can be associated by duality to a BSDE, which then characterizes the value of the original problem as well

Meal pattern among Norwegian primary-school children and longitudinal associations between meal skipping and weight status

Objective: To investigate meal pattern longitudinally and explore whether meal skipping was associated with overweight among Norwegian children and adolescents. Design: Longitudinal study. Children’s meal frequencies were reported by their parents using a retrospective FFQ. Weight and height were measured by public health nurses. Descriptive data comparing 4th and 7th grade were analysed by paired-sample t tests for continuous variables and x2 tests for categorical variables. Odds ratio estimates, including confidence intervals, with BMI category (normal/overweight) as the dependent variable, were determined through logistic regression analyses. Setting: Primary schools, Telemark County, Norway. Subjects: A cohort of 428 Norwegian boys and girls; 4th graders in 2007, 7th graders in 2010. Results: The number of children eating four main meals per day (regular meal frequency) decreased from 4th grade (47 %) to 7th grade (38 %; P 5 0?001). Those who ate regular meals in 4th grade but not in 7th grade had higher odds (OR 5 3?1; 95 % CI 1?1, 9?0) of being overweight in 7th grade after adjusting for gender, maternal education and physical activity, but the odds ratio was not statistically significant after adjusting for overweight in 4th grade (OR 5 2?8; 95 % CI 0?7, 11?6). Conclusions: The present study showed significant increases in overall meal skipping among children between 4th and 7th grade. The results indicate an association between overweight and meal skipping, but additional prospective and longitudinal analyses and intervention trials are warranted to confirm this relationship.publishedVersio

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

Tectono-stratigraphic response of the Sandino Forearc Basin (N-Costa Rica and W-Nicaragua) to episodes of rough crust and oblique subduction

The southern Central American active margin is a world-class site where past and present subduction processes have been extensively studied. Tectonic erosion/accretion and oblique/orthogonal subduction are thought to alternate in space and time along the Middle American Trench. These processes may cause various responses in the upper plate, such as uplift/subsidence, deformation, and volcanic arc migration/ shut-off. We present an updated stratigraphic framework of the Late Cretaceous– Cenozoic Sandino Forearc Basin (SFB) which provides evidence of sedimentary response to tectonic events. Since its inception, the basin was predominantly filled with deep-water volcaniclastic deposits. In contrast, shallow-water deposits appeared episodically in the basin record and are considered as tectonic event markers. The SFB stretches for about 300 km and varies in thickness from 5 km (southern part) to about 16 km (northern part). The drastic, along-basin, thickness variation appears to be the result of (1) differential tectonic evolutions and (2) differential rates of sediment supply. (1) The northern SFB did not experience major tectonic events. In contrast, the reduced thickness of the southern SFB (5 km) is the result of at least four uplift phases related to the collision/accretion of bathymetric reliefs on the incoming plate: (i) the accretion of a buoyant oceanic plateau (Nicoya Complex) during the middle Campanian; (ii) the collision of an oceanic plateau (?) during the late Danian–Selandian; (iii) the collision/accretion of seamounts during the late Eocene–early Oligocene; (iv) the collision of seamounts and ridges during the Pliocene–Holocene. (2) The northwestward thickening of the SFB may have been enhanced by high sediment supply in the Fonseca Gulf area which reflects sourcing from wide, high relief drainage basins. In contrast, sedimentary input has possibly been lower along the southern SFB, due to the proximity of the narrow, lowland isthmus of southern Central America. Moreover, two phases of strongly oblique subduction affected the margin, producing strike-slip faulting in the forearc basin: (1) prior to the Farallon Plate breakup, an Oligocene transpressional phase caused deformation and uplift of the basin depocenter, triggering shallowing-upward of the Nicaraguan Isthmus in the central and northern SFB; (2) a Pleistocene–Holocene transtensional phase drives the NW-directed motion of a forearc sliver and reactivation of the graben-bounding faults of the late Neogene Nicaraguan Depression. We discuss arguments in favour of a Pliocene development of the Nicaraguan Depression and propose that the Nicaraguan Isthmus, which is the apparent rift shoulder of the depression, represents a structure inherited from the Oligocene transpressional phase

The prevalence of obesity in children with autism: a secondary data analysis using nationally representative data from the National Survey of Children's Health

<p>Abstract</p> <p>Background</p> <p>The prevalence of childhood obesity has increased dramatically in the last two decades and numerous efforts to understand, intervene on, and prevent this significant threat to children's health are underway for many segments of the pediatric population. Understanding the prevalence of obesity in populations of children with developmental disorders is an important undertaking, as the factors that give rise to obesity may not be the same as for typically developing children, and because prevention and treatment efforts may need to be tailored to meet their needs and the needs of their families. The goal of the current study was to estimate the prevalence of obesity in children and adolescents with autism.</p> <p>Methods</p> <p>This study was a secondary data analysis of cross-sectional nationally representative data collected by telephone interview of parents/guardians on 85,272 children ages 3-17 from the 2003-2004 National Survey of Children's Health (NSCH). Autism was determined by response to the question, "Has a doctor or health professional ever told you that your child has autism?" Children and adolescents were classified as obese accordingto CDC guidelines for body mass index (BMI) for age and sex.</p> <p>Results</p> <p>The prevalence of obesity in children with autism was 30.4% compared to 23.6% of children without autism (p = .075). The unadjusted odds of obesity in children with autism was 1.42 (95% confidence interval (CI): 1.00, 2.02, p = .052) compared to children without autism.</p> <p>Conclusions</p> <p>Based on US nationally representative data, children with autism have a prevalence of obesity at least as high as children overall. These findings suggest that additional research is warranted to understand better the factors that influence the development of obesity in this population of children.</p