Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

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

Analytical solution of a model for complex food webs

We investigate numerically and analytically a recently proposed model for food webs [Nature {\bf 404}, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.Comment: 4 pages (RevTeX). Final versio

Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

Locomotion speed of the benthic foraminifer Ammonia tepida exposed to different nitrogen and carbon sources

Ammonia tepida is a dominant benthic foraminifer colonizing intertidal mudflat sediments. Horizontal locomotion speeds were monitored using time-lapse image analysis over 6 and 24 h. Experimental conditions were based on foraminifera exposed to dry sediment re-suspended in artificial sea water (ASW) without any nutrient addition (condition DS), to combusted sediment re-suspended in in ASW also without any nutrient addition (condition CS), or to combusted sediment re-suspended in ASW enriched with either: nitrate, urea, glucose, soil extract (SE), extracellular polymeric substances (EPS), benthic diatoms (Entomoneis paludosa) or natural microphytobenthic assemblages (MPB). Significant differences were already measured after 6 h between A. tepida mean locomotion speeds at the different experimental conditions. However, differences were clearer after 24 h where the slowest A. tepida mean locomotion speed was measured in specimens placed in CS (1.00 ± 0.30 mm h− 1) and the highest mean locomotion speed in DS (2.99 ± 0.22 mm h− 1). Three different groups were defined according to their locomotion speed, (1) foraminifera exposed to DS had a locomotion speed significantly higher than all other conditions, (2) foraminifera placed in conditions enriched in SE, Glucose, Urea and EPS had intermediary locomotion speeds (1.8–2.5 mm h− 1), and (3) conditions with foraminifera showing the lowest locomotion speeds (1–1.6 mm h− 1) were CS, nitrate, MPB and E. paludosa. Thus, foraminifera exposed to organic matter (DS, SE, Glucose and Urea) showed faster locomotion speeds than foraminifera exposed to inorganic matter (CS, nitrate) or live preys (E. paludosa, MPB). Dissolved organic matter enrichment enhanced foraminifera locomotion speed, which might be a behavioural response to satisfy their carbon and/or nitrogen requirements, and the lowest locomotion speed observed when feeding on live preys might be a consequence of longer time required for live prey phagocytosis

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

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page

Multipartite entanglement in 2 x 2 x n quantum systems

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure