779 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
Lp solutions of backward stochastic differential equations
AbstractIn this paper, we are interested in solving backward stochastic differential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions in Lp p>1, extending the results of El Karoui et al. (Math. Finance 7(1) (1997) 1) to the case where the monotonicity conditions of Pardoux (Nonlinear Analysis; Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic Publishers, Dordrecht, pp. 503â549) are satisfied. We consider both a fixed and a random time interval. In the last section, we obtain, under an additional assumption, an existence and uniqueness result for BSDEs on a fixed time interval, when the data are only in L1
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
Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider
This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the Ï(4S), Ï(3S), and Ï(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-âe+e- and (for the Ï(4S) only) e+e-âÎŒ+ÎŒ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-âe+e- and e+e-âÎŒ+ÎŒ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the Ï(3S) and Ï(2S) resonances, an additional uncertainty arises due to Ïâe+e-X background. For data collected off the Ï resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the Ï(4S), 0.58% (0.72%) for the Ï(3S), and 0.68% (0.88%) for the Ï(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat Ă lâEnergie Atomique and Institut National de Physique NuclĂ©aire et de Physiquedes Particules (France), the Bundesministerium fĂŒr Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e InnovaciĂłn (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)
Improved Limits on decays to invisible final states
We establish improved upper limits on branching fractions for B0 decays to
final States 10 where the decay products are purely invisible (i.e., no
observable final state particles) and for final states where the only visible
product is a photon. Within the Standard Model, these decays have branching
fractions that are below the current experimental sensitivity, but various
models of physics beyond the Standard Model predict significant contributions
for these channels. Using 471 million BB pairs collected at the Y(4S) resonance
by the BABAR experiment at the PEP-II e+e- storage ring at the SLAC National
Accelerator Laboratory, we establish upper limits at the 90% confidence level
of 2.4x10^-5 for the branching fraction of B0-->Invisible and 1.7x10^-5 for the
branching fraction of B0-->Invisible+gammaComment: 8 pages, 3 postscript figures, submitted to Phys. Rev. D (Rapid
Communications
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Measurement of B(B-->X_s {\gamma}), the B-->X_s {\gamma} photon energy spectrum, and the direct CP asymmetry in B-->X_{s+d} {\gamma} decays
The photon spectrum in B --> X_s {\gamma} decay, where X_s is any strange
hadronic state, is studied using a data sample of (382.8\pm 4.2) \times 10^6
e^+ e^- --> \Upsilon(4S) --> BBbar events collected by the BABAR experiment at
the PEP-II collider. The spectrum is used to measure the branching fraction B(B
--> X_s \gamma) = (3.21 \pm 0.15 \pm 0.29 \pm 0.08)\times 10^{-4} and the
first, second, and third moments = 2.267 \pm 0.019 \pm 0.032 \pm
0.003 GeV,, )^2> = 0.0484 \pm 0.0053 \pm 0.0077 \pm
0.0005 GeV^2, and )^3> = -0.0048 \pm 0.0011 \pm 0.0011
\pm 0.0004 GeV^3, for the range E_\gamma > 1.8 GeV, where E_{\gamma} is the
photon energy in the B-meson rest frame. Results are also presented for
narrower E_{\gamma} ranges. In addition, the direct CP asymmetry A_{CP}(B -->
X_{s+d} \gamma) is measured to be 0.057 \pm 0.063. The spectrum itself is also
unfolded to the B-meson rest frame; that is the frame in which theoretical
predictions for its shape are made.Comment: 37 pages, 19 postscript figures, submitted to Phys. Rev. D. No
analysis or results have changed from previous version. Some changes to
improve clarity based on interactions with Phys. Rev. D referees, including
one new Figure (Fig. 13), and some minor wording/punctuation/spelling
mistakes fixe
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Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
A precise measurement of the cross section of the process
from threshold to an energy of 3GeV is obtained
with the initial-state radiation (ISR) method using 232fb of data
collected with the BaBar detector at center-of-mass energies near
10.6GeV. The ISR luminosity is determined from a study of the leptonic process
, which is found to agree with the
next-to-leading-order QED prediction to within 1.1%. The cross section for the
process is obtained with a systematic uncertainty
of 0.5% in the dominant resonance region. The leading-order hadronic
contribution to the muon magnetic anomaly calculated using the measured
cross section from threshold to 1.8GeV is .Comment: 58 pages, 56 figures, to be submitted to Phys. Rev.
Search for lepton-number violating processes in B+ -> h- l+ l+ decays
We have searched for the lepton-number violating processes B+ -> h- l+ l+
with h- = K-/pi- and l+ = e+/mu+, using a sample of 471+/-3 million BBbar
events collected with the BaBar detector at the PEP-II e+e- collider at the
SLAC National Accelerator Laboratory. We find no evidence for these decays and
place 90% confidence level upper limits on their branching fractions Br(B+ ->
pi- e+ e+) K- e+ e+) pi-
mu+ mu+) K- mu+ mu+) < 6.7 x 10^{-8}.Comment: 8 pages, 4 postscript figures, submitted to Phys. Rev. D. R
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Measurement of the Time-Dependent CP Asymmetry of Partially Reconstructed B0->D*+D*- Decays
We present a new measurement of the time-dependent CP asymmetry of B0->D*+D*-
decays using (471+-5) million BBbar pairs collected with the BaBar detector at
the PEP-II B Factory at the SLAC National Accelerator Laboratory. Using the
technique of partial reconstruction, we measure the time-dependent CP asymmetry
parameters S=-0.34+-0.12+-0.05$ and C=+0.15+-0.09+-0.04. Using the value for
the CP-odd fraction R_perp=0.158+-0.028+-0.006, previously measured by BaBar
with fully reconstructed B0->D*+D*- events, we extract the CP-even components
S+=-0.49+-0.18+-0.07+-0.04 and C+=+0.15+-0.09+-0.04. In each case, the first
uncertainty is statistical and the second is systematic; the third uncertainty
on S+ is the contribution from the uncertainty on R_perp. The measured value of
the CP-even component S+ is consistent with the value of sin(2Beta) measured in
b->(ccbar)s transitions, and with the Standard Model expectation of small
penguin contributions.Comment: 17 pages, 7 figures, submitted to Physical Review
Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
We report the results of a study of the exclusive charmless semileptonic
decays, B^0 --> pi^- l^+ nu, B^+ --> pi^0 l^+ nu, B^+ --> omega l^+ nu, B^+ -->
eta l^+ nu and B^+ --> eta^' l^+ nu, (l = e or mu) undertaken with
approximately 462x10^6 B\bar{B} pairs collected at the Upsilon(4S) resonance
with the BABAR detector. The analysis uses events in which the signal B decays
are reconstructed with a loose neutrino reconstruction technique. We obtain
partial branching fractions in several bins of q^2, the square of the momentum
transferred to the lepton-neutrino pair, for B^0 --> pi^- l^+ nu, B^+ --> pi^0
l^+ nu, B^+ --> omega l^+ nu and B^+ --> eta l^+ nu. From these distributions,
we extract the form-factor shapes f_+(q^2) and the total branching fractions
BF(B^0 --> pi^- l^+ nu) = (1.45 +/- 0.04_{stat} +/- 0.06_{syst})x10^-4
(combined pi^- and pi^0 decay channels assuming isospin symmetry), BF(B^+ -->
omega l^+ nu) = (1.19 +/- 0.16_{stat} +/- 0.09_{syst})x10^-4 and BF(B^+ --> eta
l^+ nu) = (0.38 +/- 0.05_{stat} +/- 0.05_{syst})x10^-4. We also measure BF(B^+
--> eta^' l^+ nu) = (0.24 +/- 0.08_{stat} +/- 0.03_{syst})x10^-4. We obtain
values for the magnitude of the CKM matrix element V_{ub} by direct comparison
with three different QCD calculations in restricted q^2 ranges of B --> pi l^+
nu decays. From a simultaneous fit to the experimental data over the full q^2
range and the FNAL/MILC lattice QCD predictions, we obtain |V_{ub}| = (3.25 +/-
0.31)x10^-3, where the error is the combined experimental and theoretical
uncertainty.Comment: 35 pages, 14 figures, submitted to PR
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