395 research outputs found
Sharp adaptive estimation of the drift function for ergodic diffusions
The global estimation problem of the drift function is considered for a large
class of ergodic diffusion processes. The unknown drift is supposed
to belong to a nonparametric class of smooth functions of order , but
the value of is not known to the statistician. A fully data-driven
procedure of estimating the drift function is proposed, using the estimated
risk minimization method. The sharp adaptivity of this procedure is proven up
to an optimal constant, when the quality of the estimation is measured by the
integrated squared error weighted by the square of the invariant density.Comment: Published at http://dx.doi.org/10.1214/009053605000000615 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Constraints on Light Dark Matter From Core-Collapse Supernovae
We show that light ( 1 -- 30 MeV) dark matter particles can play a
significant role in core-collapse supernovae, if they have relatively large
annihilation and scattering cross sections, as compared to neutrinos. We find
that if such particles are lighter than 10 MeV and reproduce the
observed dark matter relic density, supernovae would cool on a much longer time
scale and would emit neutrinos with significantly smaller energies than in the
standard scenario, in disagreement with observations. This constraint may be
avoided, however, in certain situations for which the neutrino--dark matter
scattering cross sections remain comparatively small.Comment: 4 pages, 1 figur
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
Stein's method and exact Berry--Esseen asymptotics for functionals of Gaussian fields
We show how to detect optimal Berry--Esseen bounds in the normal
approximation of functionals of Gaussian fields. Our techniques are based on a
combination of Malliavin calculus, Stein's method and the method of moments and
cumulants, and provide de facto local (one-term) Edgeworth expansions. The
findings of the present paper represent a further refinement of the main
results proven in Nourdin and Peccati [Probab. Theory Related Fields 145 (2009)
75--118]. Among several examples, we discuss three crucial applications: (i) to
Toeplitz quadratic functionals of continuous-time stationary processes
(extending results by Ginovyan [Probab. Theory Related Fields 100 (1994)
395--406] and Ginovyan and Sahakyan [Probab. Theory Related Fields 138 (2007)
551--579]); (ii) to ``exploding'' quadratic functionals of a Brownian sheet;
and (iii) to a continuous-time version of the Breuer--Major CLT for functionals
of a fractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/09-AOP461 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
Vanishing cycles and mutation
This is the writeup of a talk given at the European Congress of Mathematics,
Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology
viewpoint.Comment: 20 pages, LaTeX2e. TeXnical problem should now be fixed, so that the
images will appear even if you download the .ps fil
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