1,206 research outputs found
Hadronic matrix elements from the lattice
Lattice matrix elements are briefly reviewed. In the quenched approximation
, and are now under good control. Experimental hints for
are noted; precise determination of
from experiment as well as from the lattice is strongly advocated.
Lattice calculations of the form factor for at relatively
large value of have made good progress and should be useful in
conjunction with precise measurement of the differential spectra expected from
-factories. Recent attempt at using staggered quarks is
briefly discussed; use of non-perturbative renormalization, improved actions
and operators with staggered quarks is emphasized. Due to the good chiral
behavior of domain wall quarks it would be useful to study with
this discretization.Comment: 8 pages, Invited talk given at the Third International Conference on
B Physics and CP Violation, Taipei, Dec. 3-7, 9
CP Violation Highlights: Circa 2005
Recent highlights in CP violation phenomena are reviewed. B-factory results
imply that CP-violation phase in the CKM matrix is the dominant contributor to
the observed CP violation in K and B-physics. Deviations from the predictions
of the CKM-paradigm due to beyond the Standard Model CP-odd phase are likely to
be a small perturbation. Therefore, large data sample of clean B's will be
needed. Precise determination of the unitarity triangle, along with time
dependent CP in penguin dominated hadronic and radiative modes are discussed.
Null tests in B, K and top-physics and separate determination of the
K-unitarity triangle are also emphasized.Comment: Invited talk at "Results and Perspectives in Particle Physics", La
Thuile, Acosta Valley, Feb27-Mar3, 200
Existence of optimal controls for singular control problems with state constraints
We establish the existence of an optimal control for a general class of
singular control problems with state constraints. The proof uses weak
convergence arguments and a time rescaling technique. The existence of optimal
controls for Brownian control problems \citehar, associated with a broad family
of stochastic networks, follows as a consequence.Comment: Published at http://dx.doi.org/10.1214/105051606000000556 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Singular control with state constraints on unbounded domain
We study a class of stochastic control problems where a cost of the form
\begin{equation}\mathbb{E}\int_{[0,\infty)}e^{-\beta s}[\ell(X_s)
ds+h(Y^{\circ}_s) d|Y|_s]\end{equation} is to be minimized over control
processes whose increments take values in a cone of
, keeping the state process in a cone of
, . Here, , is a Brownian motion with
drift and covariance , is a fixed matrix, and is
the Radon--Nikodym derivative . Let where denotes the gradient. Solutions to the corresponding
dynamic programming PDE,
\begin{equation}[(\mathcal{L}+\beta)f-\ell]\vee\sup_{y\in\mathbb{Y}:|Gy|=1
}[-Gy\cdot Df-h(y)]=0,\end{equation} on are considered with a
polynomial growth condition and are required to be supersolution up to the
boundary (corresponding to a ``state constraint'' boundary condition on
). Under suitable conditions on the problem data, including
continuity and nonnegativity of and , and polynomial growth of
, our main result is the unique viscosity-sense solvability of the PDE by
the control problem's value function in appropriate classes of functions. In
some cases where uniqueness generally fails to hold in the class of functions
that grow at most polynomially (e.g., when ), our methods provide
uniqueness within the class of functions that, in addition, have compact level
sets. The results are new even in the following special cases: (1) The
one-dimensional case , ; (2) The
first-order case ; (3) The case where and are linear. The
proofs combine probabilistic arguments and viscosity solution methods. Our
framework covers a wide range of diffusion control problems that arise from
queueing networks in heavy traffic.Comment: Published at http://dx.doi.org/10.1214/009117906000000359 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Some Fluctuation Results for Weakly Interacting Multi-type Particle System
A collection of -diffusing interacting particles where each particle
belongs to one of different populations is considered. Evolution equation
for a particle from population depends on the empirical measures of
particle states corresponding to the various populations and the form of this
dependence may change from one population to another. In addition, the drift
coefficients in the particle evolution equations may depend on a factor that is
common to all particles and which is described through the solution of a
stochastic differential equation coupled, through the empirical measures, with
the -particle dynamics. We are interested in the asymptotic behavior as
. Although the full system is not exchangeable, particles in the
same population have an exchangeable distribution. Using this structure, one
can prove using standard techniques a law of large numbers result and a
propagation of chaos property. In the current work we study fluctuations about
the law of large number limit. For the case where the common factor is absent
the limit is given in terms of a Gaussian field whereas in the presence of a
common factor it is characterized through a mixture of Gaussian distributions.
We also obtain, as a corollary, new fluctuation results for disjoint
sub-families of single type particle systems, i.e. when . Finally, we
establish limit theorems for multi-type statistics of such weakly interacting
particles, given in terms of multiple Wiener integrals.Comment: 47 page
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