Regularity of Nash payoffs of Markovian nonzero-sum stochastic differential games

In this paper we deal with the problem of existence of a smooth solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in unbounded domains either in the case of continuous generators or for discontinuous ones. In each case we show the existence of a smooth solution of the system. As a consequence, we show that the game has smooth Nash payoffs which are given by means of the solution of the HJBI system and the stochastic process which governs the dynamic of the controlled system.Comment: To appear in "Stochastic

The Hubble Deep Field Reveals a Supernova at z~0.95

We report the discovery of a variable object in the Hubble Deep Field North (HDF-N) which has brightened, during the 8.5 days sampled by the data, by more than 0.9 mag in I and about 0.7 mag in V, remaining stable in B. Subsequent observations of the HDF-N show that two years later this object has dimmed back to about its original brightness in I. The colors of this object, its brightness, its time behavior in the various filters and the evolution of its morphology are consistent with being a Type Ib supernova in a faint galaxy at z~0.95.Comment: 5 pages including 2 figures. Accepted for publication in MNRA

The ergodic problem for some subelliptic operators with unbounded coefficients

We study existence and uniqueness of the invariant measure for a stochastic process with degenerate diffusion, whose infinitesimal generator is a linear subelliptic operator in the whole space R N with coefficients that may be unbounded. Such a measure together with a Liouville-type theorem will play a crucial role in two applications: the ergodic problem studied through stationary problems with vanishing discount and the long time behavior of the solution to a parabolic Cauchy problem. In both cases, the constants will be characterized in terms of the invariant measure

Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations

We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$ where $\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitable deterministic Hamilton-Jacobi problem

LSD and AMAZE: the mass-metallicity relation at z>3

We present the first results on galaxy metallicity evolution at z>3 from two projects, LSD (Lyman-break galaxies Stellar populations and Dynamics) and AMAZE (Assessing the Mass Abundance redshift Evolution). These projects use deep near-infrared spectroscopic observations of a sample of ~40 LBGs to estimate the gas-phase metallicity from the emission lines. We derive the mass-metallicity relation at z$>$3 and compare it with the same relation at lower redshift. Strong evolution from z=0 and z=2 to z=3 is observed, and this finding puts strong constrains on the models of galaxy evolution. These preliminary results show that the effective oxygen yields does not increase with stellar mass, implying that the simple outflow model does not apply at z>3.Comment: 5 pages, to appear in the IAUS 255 conference proceedings: "Low-Metallicity Star Formation: from the First Stars to Dwarf Galaxies", L.K. Hunt, S. Madden and R. Schneider ed