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

MPGD's spatial and energy resolution studies with an adjustable point-like electron source

11th Vienna Conference on Instrumentation (February 2007) , to appear in the Proceedings (NIM A)International audienceMicropattern Gaseous Detectors (MPGD), like Micromegas or GEM, are used or foreseen in particle physics experiments for which a very good spatial resolution is required. We have developed an experimental method to separate the contribution of the transverse diffusion and the multiplication process by varying the number of primary electrons generated by a point-like source. A pulsed nitrogen laser is focused by an optical set-up on the drift electrode which is made of a thin metal layer deposited on a quartz lamina. The number of primary electrons can be adjusted from a few to several thousands on a spot which transverse size is less than $100 \mu m$ RMS. The detector can be positioned with an accuracy of $1\mu m$ by a motorized three dimensional system. This method was applied to a small Micromegas detector with a gain set between $10^3$ and $2.10^4$ and an injection of 60 to 2000 photoelectrons. Spatial resolutions as small as $5\mu m$ were measured with 2000 primary electrons. An estimation of the upper limit of the relative gain variance can be obtained from the measurements

Spatial Resolution of a Micromegas-TPC Using the Charge Dispersion Signal

The Time Projection Chamber (TPC) for the International Linear Collider will need to measure about 200 track points with a resolution close to 100 $\mu$m. A Micro Pattern Gas Detector (MPGD) readout TPC could achieve the desired resolution with existing techniques using sub-millimeter width pads at the expense of a large increase in the detector cost and complexity. We have recently applied a new MPGD readout concept of charge dispersion to a prototype GEM-TPC and demonstrated the feasibility of achieving good resolution with pads similar in width to the ones used for the proportional wire TPC. The charge dispersion studies were repeated with a Micromegas TPC amplification stage. We present here our first results on the Micromegas-TPC resolution with charge dispersion. The TPC resolution with the Micromegas readout is compared to our earlier GEM results and to the resolution expected from electron statistics and transverse diffusion in a gaseous TPC.Comment: 5 pages, 8 figures, to appar in the Proceedings of the 2005 International Linear Collider Workshop (LCWS05), Stanford, 18-22 March 200

Micromegas TPC studies at high magnetic fields using the charge dispersion signal

The International Linear Collider (ILC) Time Projection Chamber (TPC) transverse space-point resolution goal is 100 microns for all tracks including stiff 90 degree tracks with the full 2 meter drift. A Micro Pattern Gas Detector (MPGD) readout TPC can achieve the target resolution with existing techniques using 1 mm or narrower pads at the expense of increased detector cost and complexity. The new MPGD readout technique of charge dispersion can achieve good resolution without resorting to narrow pads. This has been demonstrated previously for 2 mm x 6 mm pads with GEMs and Micromegas in cosmic ray tests and in a KEK beam test in a 1 Tesla magnet. We have recently tested a Micromegas-TPC using the charge dispersion readout concept in a high field super-conducting magnet at DESY. The measured Micromegas gain was found to be constant within 0.5% for magnetic fields up to 5 Tesla. With the strong suppression of transverse diffusion at high magnetic fields, we measure a flat 50 micron resolution at 5 Tesla over the full 15 cm drift length of our prototype TPC.Comment: 7 pages, 3 figure

Progress on a spherical TPC for low energy neutrino detection

The new concept of the spherical TPC aims at relatively large target masses with low threshold and background, keeping an extremely simple and robust operation. Such a device would open the way to detect the neutrino-nucleus interaction, which, although a standard process, remains undetected due to the low energy of the neutrino-induced nuclear recoils. The progress in the development of the fist 1 m$^3$ prototype at Saclay is presented. Other physics goals of such a device could include supernova detection, low energy neutrino oscillations and study of non-standard properties of the neutrino, among others.Comment: 3 pages, talk given at the 9th Workshop on Topics in Astroparticle and Underground Physics, Zaragoza, September 10-1

Calibration and First light of the Diabolo photometer at the Millimetre and Infrared Testa Grigia Observatory

We have designed and built a large-throughput dual channel photometer, Diabolo. This photometer is dedicated to the observation of millimetre continuum diffuse sources, and in particular, of the Sunyaev-Zel'dovich effect and of anisotropies of the 3K background. We describe the optical layout and filtering system of the instrument, which uses two bolometric detectors for simultaneous observations in two frequency channels at 1.2 and 2.1 mm. The bolometers are cooled to a working temperature of 0.1 K provided by a compact dilution cryostat. The photometric and angular responses of the instrument are measured in the laboratory. First astronomical light was detected in March 1995 at the focus of the new Millimetre and Infrared Testa Grigia Observatory (MITO) Telescope. The established sensitivity of the system is of 7 mK_RJ s^1/2$. For a typical map of at least 10 beams, with one hour of integration per beam, one can achieve the rms values of y_SZ ~ 7 10^-5 and the 3K background anisotropy Delta T/T ~ 7 10^-5, in winter conditions. We also report on a novel bolometer AC readout circuit which allows for the first time total power measurements on the sky. This technique alleviates (but does not forbid) the use of chopping with a secondary mirror. This technique and the dilution fridge concept will be used in future scan--modulated space instrument like the ESA Planck mission project.Comment: 10 pages, LaTeX, 12 figures, accepted for publication in Astronomy and Astrophysics Supplement Serie

On Optimal Stopping and Impulse Control with Constraint

The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact