49,297 research outputs found
Aberration in qualitative multilevel designs
Generalized Word Length Pattern (GWLP) is an important and widely-used tool
for comparing fractional factorial designs. We consider qualitative factors,
and we code their levels using the roots of the unity. We write the GWLP of a
fraction using the polynomial indicator function, whose
coefficients encode many properties of the fraction. We show that the
coefficient of a simple or interaction term can be written using the counts of
its levels. This apparently simple remark leads to major consequence, including
a convolution formula for the counts. We also show that the mean aberration of
a term over the permutation of its levels provides a connection with the
variance of the level counts. Moreover, using mean aberrations for symmetric
designs with prime, we derive a new formula for computing the GWLP of
. It is computationally easy, does not use complex numbers and
also provides a clear way to interpret the GWLP. As case studies, we consider
non-isomorphic orthogonal arrays that have the same GWLP. The different
distributions of the mean aberrations suggest that they could be used as a
further tool to discriminate between fractions.Comment: 16 pages, 1 figur
Solar sensor having coarse and fine sensing with matched preirradiated cells and method of selecting cells Patent
Solar sensor with coarse and fine sensing elements for matching preirradiated cells on degradation rate
The strong predictable representation property in initially enlarged filtrations under the density hypothesis
We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of L. Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information
No-arbitrage conditions and absolutely continuous changes of measure
We study the stability of several no-arbitrage conditions with respect to
absolutely continuous, but not necessarily equivalent, changes of measure. We
first consider models based on continuous semimartingales and show that
no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in
the context of general semimartingale models, we show that an absolutely
continuous change of measure does never introduce arbitrages of the first kind
as long as the change of measure density process can reach zero only
continuously.Comment: 14 pages. Arbitrage, Credit and Informational Risks (C. Hillairet, M.
Jeanblanc and Y. Jiao, eds.), Peking University Series in Mathematics, Vol.
6, World Scientific, 201
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