2,426 research outputs found
On a class of self-similar processes with stationary increments in higher order Wiener chaoses
We study a class of self-similar processes with stationary increments
belonging to higher order Wiener chaoses which are similar to Hermite
processes. We obtain an almost sure wavelet-like expansion of these processes.
This allows us to compute the pointwise and local H\"older regularity of sample
paths and to analyse their behaviour at infinity. We also provide some results
on the Hausdorff dimension of the range and graphs of multidimensional
anisotropic self-similar processes with stationary increments defined by
multiple Wiener integrals.Comment: 22 page
Directly Imaging Tidally Powered Migrating Jupiters
Upcoming direct-imaging experiments may detect a new class of long-period,
highly luminous, tidally powered extrasolar gas giants. Even though they are
hosted by ~ Gyr-"old" main-sequence stars, they can be as "hot" as young
Jupiters at ~100 Myr, the prime targets of direct-imaging surveys. They are on
years-long orbits and presently migrating to "feed" the "hot Jupiters." They
are expected from "high-e" migration mechanisms, in which Jupiters are excited
to highly eccentric orbits and then shrink semi-major axis by a factor of
~10-100 due to tidal dissipation at close periastron passages. The dissipated
orbital energy is converted to heat, and if it is deposited deep enough into
the atmosphere, the planet likely radiates steadily at luminosity L ~ 100-1000
L_Jup(2 x 10-7-2 x 10-6 L_Sun) during a typical ~ Gyr migration timescale.
Their large orbital separations and expected high planet-to-star flux ratios in
IR make them potentially accessible to high-contrast imaging instruments on 10
m class telescopes. ~10 such planets are expected to exist around FGK dwarfs
within ~50 pc. Long-period radial velocity planets are viable candidates, and
the highly eccentric planet HD 20782b at maximum angular separation ~0.''08 is
a promising candidate. Directly imaging these tidally powered Jupiters would
enable a direct test of high-e migration mechanisms. Once detected, the
luminosity would provide a direct measurement of the migration rate, and
together with mass (and possibly radius) estimate, they would serve as a
laboratory to study planetary spectral formation and tidal physics.Comment: Updated to match the published version (with a figure
On Stein's Method for Infinitely Divisible Laws With Finite First Moment
We present, in a unified way, a Stein methodology for infinitely divisible
laws (without Gaussian component) having finite first moment. Based on a
correlation representation, we obtain a characterizing non-local Stein operator
which boils down to classical Stein operators in specific examples. Thanks to
this characterizing operator, we introduce various extensions of size bias and
zero bias distributions and prove that these notions are closely linked to
infinite divisibility. Combined with standard Fourier techniques, these
extensions also allow obtaining explicit rates of convergence for compound
Poisson approximation in particular towards the symmetric -stable
distribution. Finally, in the setting of non-degenerate self-decomposable laws,
by semigroup techniques, we solve the Stein equation induced by the
characterizing non-local Stein operator and obtain quantitative bounds in weak
limit theorems for sums of independent random variables going back to the work
of Khintchine and L\'evy.Comment: 58 pages. Minor changes and new results in Sections 5 and
A stroll along the gamma
We provide the first in-depth study of the "smart path" interpolation between
an arbitrary probability measure and the gamma-
distribution. We propose new explicit representation formulae for the ensuing
process as well as a new notion of relative Fisher information with a gamma
target distribution. We use these results to prove a differential and an
integrated De Bruijn identity which hold under minimal conditions, hereby
extending the classical formulae which follow from Bakry, Emery and Ledoux's
-calculus. Exploiting a specific representation of the "smart path", we
obtain a new proof of the logarithmic Sobolev inequality for the gamma law with
as well as a new type of HSI inequality linking relative
entropy, Stein discrepancy and standardized Fisher information for the gamma
law with .Comment: Typos correcte
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