653 research outputs found
The Heckman-Opdam Markov processes
We introduce and study the natural counterpart of the Dunkl Markov processes
in a negatively curved setting. We give a semimartingale decomposition of the
radial part, and some properties of the jumps. We prove also a law of large
numbers, a central limit theorem, and the convergence of the normalized process
to the Dunkl process. Eventually we describe the asymptotic behavior of the
infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric
spaces setting in \cite{ABJ}
On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes
Firstly, we compute the distribution function for the hitting time of a
linear time-dependent boundary by a
reflecting Brownian motion. The main tool hereby is Doob's formula which gives
the probability that Brownian motion started inside a wedge does not hit this
wedge. Other key ingredients are the time inversion property of Brownian motion
and the time reversal property of diffusion bridges. Secondly, this methodology
can also be applied for the three dimensional Bessel process. Thirdly, we
consider Bessel bridges from 0 to 0 with dimension parameter and
show that the probability that such a Bessel bridge crosses an affine boundary
is equal to the probability that this Bessel bridge stays below some fixed
value.Comment: 32 pages, 2 figure
Rates of convergence of a transient diffusion in a spectrally negative L\'{e}vy potential
We consider a diffusion process in a random L\'{e}vy potential
which is a solution of the informal stochastic differential
equation \begin{eqnarray*}\cases{dX_t=d\beta_t-{1/2}\mathbb{V}'(X_t) dt,\cr
X_0=0,}\end{eqnarray*} ( B. M. independent of ). We study
the rate of convergence when the diffusion is transient under the assumption
that the L\'{e}vy process does not possess positive jumps. We
generalize the previous results of Hu--Shi--Yor for drifted Brownian
potentials. In particular, we prove a conjecture of Carmona: provided that
there exists such that ,
then converges to some nondegenerate distribution. These
results are in a way analogous to those obtained by Kesten--Kozlov--Spitzer for
the transient random walk in a random environment.Comment: Published in at http://dx.doi.org/10.1214/009117907000000123 the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Short-time asymptotics for marginal distributions of semimartingales
We study the short-time asymptotics of conditional expectations of smooth and
non-smooth functions of a (discontinuous) Ito semimartingale; we compute the
leading term in the asymptotics in terms of the local characteristics of the
semimartingale. We derive in particular the asymptotic behavior of call options
with short maturity in a semimartingale model: whereas the behavior of
\textit{out-of-the-money} options is found to be linear in time, the short time
asymptotics of \textit{at-the-money} options is shown to depend on the fine
structure of the semimartingale
Equilibrium for fragmentation with immigration
This paper introduces stochastic processes that describe the evolution of
systems of particles in which particles immigrate according to a Poisson
measure and split according to a self-similar fragmentation. Criteria for
existence and absence of stationary distributions are established and
uniqueness is proved. Also, convergence rates to the stationary distribution
are given. Linear equations which are the deterministic counterparts of
fragmentation with immigration processes are next considered. As in the
stochastic case, existence and uniqueness of solutions, as well as existence
and uniqueness of stationary solutions, are investigated.Comment: Published at http://dx.doi.org/10.1214/105051605000000340 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Scattering rates and lifetime of exact and boson excitons
Although excitons are not exact bosons, they are commonly treated as such
provided that their composite nature is included in effective scatterings
dressed by exchange. We here \emph{prove} that, \emph{whatever these
scatterings are}, they cannot give both the scattering rates and
the exciton lifetime , correctly: A striking factor 1/2 exists between
and the sum of 's, which originates from the
composite nature of excitons, irretrievably lost when they are bosonized. This
result, which appears as very disturbing at first, casts major doubts on
bosonization for problems dealing with \emph{interacting} excitons
Theory of spin precession monitored by laser pulse
We first predict the splitting of a spin degenerate impurity level when this
impurity is irradiated by a circularly polarized laser beam tuned in the
transparency region of a semiconductor. This splitting, which comes from
different exchange processes between the impurity electron and the virtual
pairs coupled to the pump beam, induces a spin precession around the laser beam
axis, which lasts as long as the pump pulse. It can thus be used for ultrafast
spin manipulation. This effect, which has similarities with the exciton optical
Stark effect we studied long ago, is here derived using the concepts we
developed very recently to treat many-body interactions between composite
excitons and which make the physics of this type of effects quite transparent.
They, in particular, allow to easily extend this work to other experimental
situations in which a spin rotates under laser irradiation.Comment: 12 pages + 1 figur
Peintures italiennes du patrimoine français
Une sĂ©lection de rĂ©attributions et de dĂ©couvertes rĂ©centes des services des Monuments historiques et de lâInventaire gĂ©nĂ©ral. RĂ©sumĂ© de la confĂ©rence donnĂ©e le 9 mai 2000 Ă lâInstitut national dâHistoire de lâArt, dans le cadre des « mardis » de lâInventaire. Par sa qualitĂ© et son rayonnement international, la peinture italienne constitue un sujet dâĂ©tude privilĂ©giĂ©. Depuis une trentaine dâannĂ©es, le domaine connaĂźt un renouvellement permanent, tant en Italie quâen France ou dans dâautres pay..
Zeros of Dirichlet series with periodic coefficients
Let be a periodic sequence, the meromorphic
continuation of , and the
number of zeros of , counted with their multiplicities, in the
rectangle , . We extend previous
results of Laurin\v{c}ikas, Kaczorowski, Kulas, and Steuding, by showing that
if is not of the form , where is a Dirichlet
polynomial and a Dirichlet L-function, then there exists an
such that for all , we
have for sufficiently large
, and suitable positive constants and depending on ,
, and .Comment: 12 pages, 1 figur
How to make Dupire's local volatility work with jumps
There are several (mathematical) reasons why Dupire's formula fails in the
non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the
option data works reasonably well. In this note we attempt to explain why. In
particular, we propose a regularization procedure of the option data so that
Dupire's local vol diffusion process recreates the correct option prices, even
in manifest presence of jumps
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