18,188 research outputs found
Comment on Identification with Taylor Rules: is it indeed impossible? Extended version
Cochrane (2007) points out that the Taylor rule parameters in New-Keynesian models are not identified, and thus trying to estimate them through single-equation regressions is pointless. This paper shows in contrast that this observation holds only for economies that do not display inflation inertia or habit formation. These inherent features of aggregate data allow to correctly identify the parameters of the monetary policy rule by single-equation analysis.monetary economics ;
Global Solutions for the One-Dimensional Vlasov-Maxwell System for Laser-Plasma Interaction
We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the
physical literature for studying laser-plasma interaction. This system can be
seen as a standard Vlasov equation in which the field is split in two terms: an
electrostatic field obtained from Poisson's equation and a vector potential
term satisfying a nonlinear wave equation. Both nonlinearities in the Poisson
and wave equations are due to the coupling with the Vlasov equation through the
charge density. We show global existence of weak solutions in the
non-relativistic case, and global existence of characteristic solutions in the
quasi-relativistic case. Moreover, these solutions are uniquely characterised
as fixed points of a certain operator. We also find a global energy functional
for the system allowing us to obtain -nonlinear stability of some
particular equilibria in the periodic setting
Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials
Despite their wide presence in various models in the study of collective
behaviors, explicit swarming patterns are difficult to obtain. In this paper,
special stationary solutions of the aggregation equation with power-law kernels
are constructed by inverting Fredholm integral operators or by employing
certain integral identities. These solutions are expected to be the global
energy stable equilibria and to characterize the generic behaviors of
stationary solutions for more general interactions
Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
We investigate the large-time asymptotics of nonlinear diffusion equations
in dimension , in the exponent interval , when the initial datum is of bounded second moment. Precise
rates of convergence to the Barenblatt profile in terms of the relative R\'enyi
entropy are demonstrated for finite-mass solutions defined in the whole space
when they are re-normalized at each time with respect to their own
second moment. The analysis shows that the relative R\'enyi entropy exhibits a
better decay, for intermediate times, with respect to the standard
Ralston-Newton entropy. The result follows by a suitable use of the so-called
concavity of R\'enyi entropy power
Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming
We perform an asymptotic analysis of general particle systems arising in
collective behavior in the limit of large self-propulsion and friction forces.
These asymptotics impose a fixed speed in the limit, and thus a reduction of
the dynamics to a sphere in the velocity variables. The limit models are
obtained by averaging with respect to the fast dynamics. We can include all
typical effects in the applications: short-range repulsion, long-range
attraction, and alignment. For instance, we can rigorously show that the
Cucker-Smale model is reduced to the Vicsek model without noise in this
asymptotic limit. Finally, a formal expansion based on the reduced dynamics
allows us to treat the case of diffusion. This technique follows closely the
gyroaverage method used when studying the magnetic confinement of charged
particles. The main new mathematical difficulty is to deal with measure
solutions in this expansion procedure
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