3,654 research outputs found
Some techniques on nonlinear analysis and applications
In this paper we present two different results in the context of nonlinear
analysis. The first one is essentially a nonlinear technique that, in view of
its strong generality, may be useful in different practical problems. The
second result, more technical, but also connected to the first one, is an
extension of the well-known Pietsch Domination Theorem. The last decade
witnessed the birth of different families of Pietsch Domination-type results
and some attempts of unification. Our result, that we call "full general
Pietsch Domination Theorem" is potentially a definitive Pietsch Domination
Theorem which unifies the previous versions and delimits what can be proved in
this line.The connections to the recent notion of weighted summability are
traced.Comment: 24 page
Asymptotic spectral theory for nonlinear time series
We consider asymptotic problems in spectral analysis of stationary causal
processes. Limiting distributions of periodograms and smoothed periodogram
spectral density estimates are obtained and applications to the spectral domain
bootstrap are given. Instead of the commonly used strong mixing conditions, in
our asymptotic spectral theory we impose conditions only involving
(conditional) moments, which are easily verifiable for a variety of nonlinear
time series.Comment: Published in at http://dx.doi.org/10.1214/009053606000001479 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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