Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q \geq 1$ and self-similarity parameter $H \in (\frac{1}{2}, 1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q\geq 2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $dX_t = a(b - X_t)dt +dZ_t$. Here, $a > 0$ and $b \in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.Comment: 19 pages, revised according to referee's repor

Lipschitz-continuity of the integrated density of states for Gaussian random potentials

The integrated density of states of a Schroedinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate

Offshore Migratory Corridors and Aerial Photogrammetric Body Length Comparisons of Southbound Gray Whales, Eschrichtius robustus, in the Southern California Bight, 1988–1990

Through most of their annual migration, gray whales, Eschrichtius robustus, remain within 10 km of shore, but in the Southern California Bight many individuals migrate much farther from shore. This paper summarizes aerial survey and photogrammetric efforts to determine body lengths and temporal and spatial distributions of migratory gray whales in the southern portion of the Southern California Bight. Aerial surveys were flown along 13 east–west transects between lat. 32°35′N and 33°30′N during the southbound gray whale migratory seasons of 1988–90 in the Southern California Bight. Photogrammetry was used to obtain body length estimates of animals during some of the surveys. A total of 1,878 whales in 675 groups were sighted along 25,440 km of transect distance flown and 217 body lengths were measured. Using position and heading data, three major migratory pathways or corridors in the southern portion of the bight are defined. Those migrating offshore were split almost evenly between two corridors along the west sides of Santa Catalina and San Clemente Islands. These corridors converge on the mainland coast between San Diego and the United States–Mexico border. No whales larger than 11.5 m were photographed within 30 km of the mainland coast, suggesting that smaller, and presumably younger, whales use the coastal migratory corridor through the California Bight

Affine orbifolds and rational conformal field theory extensions of W_{1+infinity}

Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear form on its Lie algebra. Any finite group $\Gamma$ of inner automorphisms or A (in particular, any finite subgroup of G) gives rise to a gauge theory with a chiral subalgebra $A^{\Gamma}\subset A$ of local observables invariant under $\Gamma$. A set of positive energy $A^{\Gamma}$ modules is constructed whose characters span, under some assumptions on $\Gamma$, a finite dimensional unitary representation of $SL(2,Z)$. We compute their asymptotic dimensions (thus singling out the nontrivial orbifold modules) and find explicit formulae for the modular transformations and hence, for the fusion rules. As an application we construct a family of rational conformal field theory (RCFT) extensions of $W_{1+\infty}$ that appear to provide a bridge between two approaches to the quantum Hall effect.Comment: 64 pages, amste

Rationality of conformally invariant local correlation functions on compactified Minkowski space

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of Minkowski space and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations.Comment: 20 pages, LATEX, amsfonts, latexsy