133,597 research outputs found
A Note on the Identifiability of Generalized Linear Mixed Models
I present here a simple proof that, under general regularity conditions, the
standard parametrization of generalized linear mixed model is identifiable. The
proof is based on the assumptions of generalized linear mixed models on the
first and second order moments and some general mild regularity conditions,
and, therefore, is extensible to quasi-likelihood based generalized linear
models. In particular, binomial and Poisson mixed models with dispersion
parameter are identifiable when equipped with the standard parametrization.Comment: 9 pages, no figure
On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
We obtain a criterion for the quasi-regularity of generalized (non-sectorial)
Dirichlet forms, which extends the result of P.J. Fitzsimmons on the
quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov)
process associated to a semi-Dirichlet form, we present sufficient conditions
for a second right process to be a standard one, having the same state space.
The above mentioned quasi-regularity criterion is then an application. The
conditions are expressed in terms of the associated capacities, nests of
compacts, polar sets, and quasi-continuity. A second application is on the
quasi-regularity of the generalized Dirichlet forms obtained by perturbing a
semi-Dirichlet form with kernels .Comment: Correction of typos and other minor change
Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity
We present new types of regularity for nonlinear generalized functions, based
on the notion of regular growth with respect to the regularizing parameter of
Colombeau's simplified model. This generalizes the notion of G^{\infty
}-regularity introduced by M. Oberguggenberger. A key point is that these
regularities can be characterized, for compactly supported generalized
functions, by a property of their Fourier transform. This opens the door to
microanalysis of singularities of generalized functions, with respect to these
regularities. We present a complete study of this topic, including properties
of the Fourier transform (exchange and regularity theorems) and relationship
with classical theory, via suitable results of embeddings.Comment: Submitted to the Journal of Mathematical Analysis and Application
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