76 research outputs found
Adaptive hypothesis testing using wavelets
Let a function f be observed with a noise. We wish to test the null hypothesis that the function is identically zero, against a composite nonparametric alternative: functions from the alternative set are separated away from zero in an integral Ž e.g., L. 2 norm and also possess some smoothness properties. The minimax rate of testing for this problem was evaluated in earlier papers by Ingster and by Lepski and Spokoiny under different kinds of smoothness assumptions. It was shown that both the optimal rate of testing and the structure of optimal Ž in rate. tests depend on smoothness parameters which are usually unknown in practical applications. In this paper the problem of adaptive Ž assumption free. testing is considered. It is shown that adaptive testing without loss of efficiency is impossible. An extra log log-factor is inessential but unavoidable payment for the adaptation. A simple adaptive test based on wavelet technique is constructed which is nearly minimax for a wide range of Besov classes. 1. Introduction. Suppos
Regression Methods in Pricing American and Bermudan Options Using Consumption Processes
Numerical algorithms for the efficient pricing of multidimensional discrete-time American and Bermudan options are constructed using regression methods and a new approach for computing upper bounds of the options' price. Using the sample space with payoffs at optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach allows the constructing of both lower and upper bounds for the price by Monte Carlo simulations. The algorithms are tested by pricing Bermudan max-calls and swaptions in the Libor market model.D.B. gratefully acknowledges the partial support of DFG through SFB 649. This work was completed while G.M. was a visitor at the Weierstrass-Institute für Angewandte Analysis und Stochastik (WIAS), Berlin, thanks to financial support from this institute and DFG (grant No. 436 RUS 17/137/05 and 436 RUS 17/24/07), which are gratefully acknowledged
Transition Density Estimation for Stochastic Differential Equations Via Forward-reverse Representations
The general reverse diffusion equations are derived and applied to the problem of transition density estimation of diffusion processes between two fixed states. For this problem we propose density estimation based on forward-reverse representations and show that this method allows essentially better results to be achieved than the usual kernel or projection estimation based on forward representations only. © 2004 ISI/BS
Some exact non-vacuum Bianchi VI0 and VII0 instantons
We report some new exact instantons in general relativity. These solutions
are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0,
with matter content of a stiff fluid. The qualitative behaviour of the
solutions is presented, and we compare it to the known results of the
corresponding self-dual Bianchi solutions. We also give axisymmetric Bianchi
VII0 solutions with an electromagnetic field.Comment: latex, 15 pages with 3 eps figure
How long before the end of inflation were observable perturbations produced?
We reconsider the issue of the number of e-foldings before the end of
inflation at which observable perturbations were generated. We determine a
plausible upper limit on that number for the standard cosmology which is around
60, with the expectation that the actual value will be up to 10 below this. We
also note a special property of the model which reduces the
uncertainties in that case and favours a higher value, giving a fairly definite
prediction of 64 e-foldings for that model. We note an extreme (and highly
implausible) situation where the number of e-foldings can be even higher,
possibly up to 100, and discuss the shortcomings of quantifying inflation by
e-foldings rather than by the change in . Finally, we discuss the impact of
non-standard evolution between the end of inflation and the present, showing
that again the expected number of e-foldings can be modified, and in some cases
significantly increased.Comment: 7 pages RevTeX4 file with one figure incorporated. Minor updates to
match version accepted by Physical Review
Relic Gravity Waves from Braneworld Inflation
We discuss a scenario in which extra dimensional effects allow a scalar field
with a steep potential to play the dual role of the inflaton as well as dark
energy (quintessence). The post-inflationary evolution of the universe in this
scenario is generically characterised by a `kinetic regime' during which the
kinetic energy of the scalar field greatly exceeds its potential energy
resulting in a `stiff' equation of state for scalar field matter . The kinetic regime precedes the radiation dominated epoch and
introduces an important new feature into the spectrum of relic gravity waves
created quantum mechanically during inflation. The gravity wave spectrum
increases with wavenumber for wavelengths shorter than the comoving horizon
scale at the commencement of the radiative regime. This `blue tilt' is a
generic feature of models with steep potentials and imposes strong constraints
on a class of inflationary braneworld models. Prospects for detection of the
gravity wave background by terrestrial and space-borne gravity wave
observatories such as LIGO II and LISA are discussed.Comment: Revised in response to referee's suggestions. Main conclusions
strengthened. 23 pages latex, 9 figures. Accepted for publication in Phys.
Rev.
Curvaton reheating: an application to braneworld inflation
The curvaton was introduced recently as a distinct inflationary mechanism for
generating adiabatic density perturbations. Implicit in that scenario is that
the curvaton offers a new mechanism for reheating after inflation, as it is a
form of energy density not diluted by the inflationary expansion. We consider
curvaton reheating in the context of a braneworld inflation model, {\em steep
inflation}, which features a novel use of the braneworld to give a new
mechanism for ending inflation. The original steep inflation model featured
reheating by gravitational particle production, but the inefficiency of that
process brings observational difficulties. We demonstrate here that the
phenomenology of steep inflation is much improved by curvaton reheating.Comment: 8 pages RevTeX4 file with two figures incorporated. Improved
referencing, matches PRD accepted versio
Aspects of Tachyonic Inflation with Exponential Potential
We consider issues related to tachyonic inflation with exponential potential.
We find exact solution of evolution equations in the slow roll limit in FRW
cosmology. We also carry out similar analysis in case of Brane assisted
tachyonic inflation. We investigate the phase space behavior of the system and
show that the dust like solution is a late time attractor. The difficulties
associated with reheating in the tachyonic model are also indicated.Comment: New References added. To appear in Phys. Rev.
Exponential potentials and cosmological scaling solutions
We present a phase-plane analysis of cosmologies containing a barotropic
fluid with equation of state , plus a scalar
field with an exponential potential where . In addition to the well-known inflationary
solutions for in which the scalar field energy density tracks that of the barotropic
fluid (which for example might be radiation or dust). We show that the scaling
solutions are the unique late-time attractors whenever they exist. The
fluid-dominated solutions, where at late times, are
always unstable (except for the cosmological constant case ). The
relative energy density of the fluid and scalar field depends on the steepness
of the exponential potential, which is constrained by nucleosynthesis to
. We show that standard inflation models are unable to solve
this `relic density' problem.Comment: 6 pages RevTeX file with four figures incorporated (uses RevTeX and
epsf). Matches published versio
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