7,796 research outputs found
Autocontinuity and convergence theorems for the Choquet integral
Our aim is to provide some convergence theorems for the Choquet integral with respect to various notions of convergence. For instance, the dominated convergence theorem for almost uniform convergence is related to autocontinuous set functions. Autocontinuity can also be related to convergence in measure, strict convergence or mean convergence. Whereas the monotone convergence theorem for almost uniform convergence is related to monotone autocontinuity, a weaker version than autocontinuity.
Quantile and Probability Curves Without Crossing
This paper proposes a method to address the longstanding problem of lack of
monotonicity in estimation of conditional and structural quantile functions,
also known as the quantile crossing problem. The method consists in sorting or
monotone rearranging the original estimated non-monotone curve into a monotone
rearranged curve. We show that the rearranged curve is closer to the true
quantile curve in finite samples than the original curve, establish a
functional delta method for rearrangement-related operators, and derive
functional limit theory for the entire rearranged curve and its functionals. We
also establish validity of the bootstrap for estimating the limit law of the
the entire rearranged curve and its functionals. Our limit results are generic
in that they apply to every estimator of a monotone econometric function,
provided that the estimator satisfies a functional central limit theorem and
the function satisfies some smoothness conditions. Consequently, our results
apply to estimation of other econometric functions with monotonicity
restrictions, such as demand, production, distribution, and structural
distribution functions. We illustrate the results with an application to
estimation of structural quantile functions using data on Vietnam veteran
status and earnings.Comment: 29 pages, 4 figure
Hamiltonian Pseudo-rotations of Projective Spaces
The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of
with the minimal possible number of periodic points
(equal to by Arnold's conjecture), called here Hamiltonian
pseudo-rotations. We prove several results on the dynamics of pseudo-rotations
going beyond periodic orbits, using Floer theoretical methods. One of these
results is the existence of invariant sets in arbitrarily small punctured
neighborhoods of the fixed points, partially extending a theorem of Le Calvez
and Yoccoz and Franks to higher dimensions. The other is a strong variant of
the Lagrangian Poincar\'e recurrence conjecture for pseudo-rotations. We also
prove the -rigidity of pseudo-rotations with exponentially Liouville mean
index vector. This is a higher-dimensional counterpart of a theorem of Bramham
establishing such rigidity for pseudo-rotations of the disk.Comment: 38 pages; final version (with minor revisions and updated
references); published Online First in Inventiones mathematica
A Dissipative Model for Hydrogen Storage: Existence and Regularity Results
We prove global existence of a solution to an initial and boundary value
problem for a highly nonlinear PDE system. The problem arises from a
thermomechanical dissipative model describing hydrogen storage by use of metal
hydrides. In order to treat the model from an analytical point of view, we
formulate it as a phase transition phenomenon thanks to the introduction of a
suitable phase variable. Continuum mechanics laws lead to an evolutionary
problem involving three state variables: the temperature, the phase parameter
and the pressure. The problem thus consists of three coupled partial
differential equations combined with initial and boundary conditions. Existence
and regularity of the solutions are here investigated by means of a time
discretization-a priori estimates-passage to the limit procedure joined with
compactness and monotonicity arguments
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
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