2,140 research outputs found
Propriété de Markov des équations stationnaires discrètes quasi-linéaires
AbstractIn this paper, we consider the stochastic discrete equation − ΔU(x)+ƒ(U(x))=A(x) where x runs over a finite domain Θ of Zd, Δ is a discretization od the Laplacian operator, {A(x)} is a sequence of i.i.d. Gaussian variables, and we impose the Dirchlet condition U(x)=0 for x∉Θ. We prove existence and uniquesness of a solution assuming monotonicity condition on ƒ, and we study the Markov property of the solution
Continued fraction solution of Krein's inverse problem
The spectral data of a vibrating string are encoded in its so-called
characteristic function. We consider the problem of recovering the distribution
of mass along the string from its characteristic function. It is well-known
that Stieltjes' continued fraction provides a solution of this inverse problem
in the particular case where the distribution of mass is purely discrete. We
show how to adapt Stieltjes' method to solve the inverse problem for a related
class of strings. An application to the excursion theory of diffusion processes
is presented.Comment: 18 pages, 2 figure
A detector interferometric calibration experiment for high precision astrometry
Context: Exoplanet science has made staggering progress in the last two
decades, due to the relentless exploration of new detection methods and
refinement of existing ones. Yet astrometry offers a unique and untapped
potential of discovery of habitable-zone low-mass planets around all the
solar-like stars of the solar neighborhood. To fulfill this goal, astrometry
must be paired with high precision calibration of the detector.
Aims: We present a way to calibrate a detector for high accuracy astrometry.
An experimental testbed combining an astrometric simulator and an
interferometric calibration system is used to validate both the hardware needed
for the calibration and the signal processing methods. The objective is an
accuracy of 5e-6 pixel on the location of a Nyquist sampled polychromatic point
spread function.
Methods: The interferometric calibration system produced modulated Young
fringes on the detector. The Young fringes were parametrized as products of
time and space dependent functions, based on various pixel parameters. The
minimization of func- tion parameters was done iteratively, until convergence
was obtained, revealing the pixel information needed for the calibration of
astrometric measurements.
Results: The calibration system yielded the pixel positions to an accuracy
estimated at 4e-4 pixel. After including the pixel position information, an
astrometric accuracy of 6e-5 pixel was obtained, for a PSF motion over more
than five pixels. In the static mode (small jitter motion of less than 1e-3
pixel), a photon noise limited precision of 3e-5 pixel was reached
On small-noise equations with degenerate limiting system arising from volatility models
The one-dimensional SDE with non Lipschitz diffusion coefficient is widely
studied in mathematical finance. Several works have proposed asymptotic
analysis of densities and implied volatilities in models involving instances of
this equation, based on a careful implementation of saddle-point methods and
(essentially) the explicit knowledge of Fourier transforms. Recent research on
tail asymptotics for heat kernels [J-D. Deuschel, P.~Friz, A.~Jacquier, and
S.~Violante. Marginal density expansions for diffusions and stochastic
volatility, part II: Applications. 2013, arxiv:1305.6765] suggests to work with
the rescaled variable : while
allowing to turn a space asymptotic problem into a small- problem
with fixed terminal point, the process satisfies a SDE in
Wentzell--Freidlin form (i.e. with driving noise ). We prove a
pathwise large deviation principle for the process as
. As it will become clear, the limiting ODE governing the
large deviations admits infinitely many solutions, a non-standard situation in
the Wentzell--Freidlin theory. As for applications, the -scaling
allows to derive exact log-asymptotics for path functionals of the process:
while on the one hand the resulting formulae are confirmed by the CIR-CEV
benchmarks, on the other hand the large deviation approach (i) applies to
equations with a more general drift term and (ii) potentially opens the way to
heat kernel analysis for higher-dimensional diffusions involving such an SDE as
a component.Comment: 21 pages, 1 figur
On Sharp Large Deviations for the bridge of a general Diffusion
We provide sharp Large Deviation estimates for the probability of exit from a
domain for the bridge of a -dimensional general diffusion process , as
the conditioning time tends to . This kind of results is motivated by
applications to numerical simulation. In particular we investigate the
influence of the drift of . It turns out that the sharp asymptotics for
the exit time probability are independent of the drift, provided enjoyes a
simple condition that is always satisfied in dimension . On the other hand,
we show that the drift can be influential if this assumption is not satisfied.
Meixner class of non-commutative generalized stochastic processes with freely independent values I. A characterization
Let be an underlying space with a non-atomic measure on it (e.g.
and is the Lebesgue measure). We introduce and study a
class of non-commutative generalized stochastic processes, indexed by points of
, with freely independent values. Such a process (field),
, , is given a rigorous meaning through smearing out
with test functions on , with being a
(bounded) linear operator in a full Fock space. We define a set
of all continuous polynomials of , and then define a con-commutative
-space by taking the closure of in the norm
, where is the vacuum in the Fock
space. Through procedure of orthogonalization of polynomials, we construct a
unitary isomorphism between and a (Fock-space-type) Hilbert space
, with
explicitly given measures . We identify the Meixner class as those
processes for which the procedure of orthogonalization leaves the set invariant. (Note that, in the general case, the projection of a
continuous monomial of oder onto the -th chaos need not remain a
continuous polynomial.) Each element of the Meixner class is characterized by
two continuous functions and on , such that, in the
space, has representation
\omega(t)=\di_t^\dag+\lambda(t)\di_t^\dag\di_t+\di_t+\eta(t)\di_t^\dag\di^2_t,
where \di_t^\dag and \di_t are the usual creation and annihilation
operators at point
A detailed spectropolarimetric analysis of the planet hosting star WASP-12
The knowledge of accurate stellar parameters is paramount in several fields
of stellar astrophysics, particularly in the study of extrasolar planets, where
often the star is the only visible component and therefore used to infer the
planet's fundamental parameters. Another important aspect of the analysis of
planetary systems is the stellar activity and the possible star-planet
interaction. Here we present a self-consistent abundance analysis of the planet
hosting star WASP-12 and a high-precision search for a structured stellar
magnetic field on the basis of spectropolarimetric observations obtained with
the ESPaDOnS spectropolarimeter. Our results show that the star does not have a
structured magnetic field, and that the obtained fundamental parameters are in
good agreement with what was previously published. In addition we derive
improved constraints on the stellar age (1.0-2.65 Gyr), mass (1.23-1.49 M/M0),
and distance (295-465 pc). WASP-12 is an ideal object to look for pollution
signatures in the stellar atmosphere. We analyse the WASP-12 abundances as a
function of the condensation temperature and compare them with those published
by several other authors on planet hosting and non-planet hosting stars. We
find hints of atmospheric pollution in WASP-12's photosphere, but are unable to
reach firm conclusions with our present data. We conclude that a differential
analysis based on WASP-12 twins will probably clarify if an atmospheric
pollution is present, the nature of this pollution and its implications in the
planet formation and evolution. We attempt also the direct detection of the
circumstellar disk through infrared excess, but without success.Comment: 49 pages, 11 figures, Accepted for publication on Ap
Intertwinings for general β Laguerre and Jacobi processes
We show that, for β≥1, the semigroups of β-Laguerre and β-Jacobi processes of different dimensions are intertwined in analogy to a similar result for β-Dyson Brownian motion recently obtained in Ramanan and Shkolnikov (Intertwinings of β-Dyson Brownian motions of different dimensions, 2016. arXiv:1608.01597). These intertwining relations generalize to arbitrary β≥1 the ones obtained for β=2 in Assiotis et al. (Interlacing diffusions, 2016. arXiv:1607.07182) between h-transformed Karlin–McGregor semigroups. Moreover, they form the key step toward constructing a multilevel process in a Gelfand–Tsetlin pattern leaving certain Gibbs measures invariant. Finally, as a by-product, we obtain a relation between general β-Jacobi ensembles of different dimensions
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