3,110 research outputs found
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
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
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
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
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
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
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
Algebraic invariants of five qubits
The Hilbert series of the algebra of polynomial invariants of pure states of
five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include
Extended Classical Over-Barrier Model for Collisions of Highly Charged Ions with Conducting and Insulating Surfaces
We have extended the classical over-barrier model to simulate the
neutralization dynamics of highly charged ions interacting under grazing
incidence with conducting and insulating surfaces. Our calculations are based
on simple model rates for resonant and Auger transitions. We include effects
caused by the dielectric response of the target and, for insulators, localized
surface charges. Characteristic deviations regarding the charge transfer
processes from conducting and insulating targets to the ion are discussed. We
find good agreement with previously published experimental data for the image
energy gain of a variety of highly charged ions impinging on Au, Al, LiF and KI
crystals.Comment: 32 pages http://pikp28.uni-muenster.de/~ducree
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