Order of convergence of regression parameter estimates in models with infinite variance

AbstractA semimartingale driven continuous time linear regression model is studied. Assumptions concerning errors allow us to consider also models with infinite variance. The order of the almost sure convergence of a class of estimates which includes least squares estimates is given. In the presence of errors with heavy tails a modification of least squares estimates is suggested and shown to be better than the latter

The Copeland measure of Condorcet choice functions

AbstractWe propose a measure to compare an arbitrary choice function with the Copeland choice function. We compute this measure for the familiar Condorcet choice functions

Spin precession and inverted Hanle effect in a semiconductor near a finite-roughness ferromagnetic interface

Although the creation of spin polarization in various non-magnetic media via electrical spin injection from a ferromagnetic tunnel contact has been demonstrated, much of the basic behavior is heavily debated. It is reported here for semiconductor/Al2O3/ferromagnet tunnel structures based on Si or GaAs that local magnetostatic fields arising from interface roughness dramatically alter and even dominate the accumulation and dynamics of spins in the semiconductor. Spin precession in the inhomogeneous magnetic fields is shown to reduce the spin accumulation up to tenfold, and causes it to be inhomogeneous and non-collinear with the injector magnetization. The inverted Hanle effect serves as experimental signature. This interaction needs to be taken into account in the analysis of experimental data, particularly in extracting the spin lifetime and its variation with different parameters (temperature, doping concentration). It produces a broadening of the standard Hanle curve and thereby an apparent reduction of the spin lifetime. For heavily doped n-type Si at room temperature it is shown that the spin lifetime is larger than previously determined, and a new lower bound of 0.29 ns is obtained. The results are expected to be general and occur for spins near a magnetic interface not only in semiconductors but also in metals, organic and carbon-based materials including graphene, and in various spintronic device structures.Comment: Final version, with text restructured and appendices added (25 pages, 9 figures). To appear in Phys. Rev.

Asymptotic Behaviour of Reduced-Order Filters

Reduced-order filters are proposed for linear and nonlinear systems and their long time behaviour is studied. Using the results of Ocone and Pardoux \cite{ocpa} on the asymptotic stability of the optimal filter with respect to its initial condition, the asymptotic efficiency of these filters is established in various cases

Asymptotic Optimality of Approximate Filters in Stochastic Systems with Colored Noises

In this report, a new interpretation of the main part of our study on asymptotic behaviour of reduced-order filters in [6] is given. Approximate filters are proposed for semi-linear and nonlinear stochastic systems with colored noises. Basically these filters are defined as those which are optimal when the noises are white. Their long time behavior is investigate- d and their asymptotic optimality is shown in two cases under some reasonable assumptions. At first the case of a system where the signal and observation dynamics are linear with respect to the state is considered; the approximate filter is a Kalman filter and the asymptotic analysis relies on a representati- on of the optimal filter which extends a formula known for a linear system with white noises and non-Gaussian initial condition. Then the case of a nonlinear system with limiting ergodic behavior is analyzed; here the approximate filter appears as the optimal filter corresponding to an incorrect prior distribution and the asymptotic study uses the results of Ocone and Pardoux on the asymptotic stability of optimal filters with respect to their initial condition

Kinematics and Convergent Tectonics of the Northwestern South American Plate During the Cenozoic

The interaction of the northern Nazca and southwestern Caribbean oceanic plates with northwestern South America (NWSA) and the collision of the Panama-Choco arc (PCA) have significant implications on the evolution of the northern Andes. Based on a quantitative kinematic reconstruction of the Caribbean and Farallon/Farallon-derived plates, we reconstructed the subducting geometries beneath NWSA and the PCA accretion to the continent. The persistent northeastward migration of the Caribbean plate relative to NWSA in Cenozoic time caused the continuous northward advance of the Farallon-Caribbean plate boundary, which in turn resulted in its progressive concave trench bending against NWSA. The increasing complexity during the Paleogene included the onset of Caribbean shallow subduction, the PCA approaching the continent, and the forced shallow Farallon subduction that ended in the fragmentation of the Farallon Plate into the Nazca and Cocos plates and the Coiba and Malpelo microplates by the late Oligocene. The convergence tectonics after late Oligocene comprised the accretional process of the PCA to NWSA, which evolved from subduction erosion of the forearc to collisional tectonics by the middle Miocene, as well as changes of convergence angle and slab dip of the Farallon-derived plates, and the attachment of the Coiba and Malpelo microplates to the Nazca plate around 9 Ma, resulting in a change of convergence directions. During the Pliocene, the Nazca slab broke at 5.5°N, shaping the modern configuration. Overall, the proposed reconstruction is supported by geophysical data and is well correlated with the magmatic and deformation history of the northern Andes

An Elementary Approach to Filtering in Systems with Fractional Brownian Observation Noise

The problem of optimal filtering is addressed for a signal observed through a possibly nonlinear channel driven by a fractional Brownian motion. An elementary and completely self-contained approach is developed. An appropriate Girsanov type result is proved and a process -- equivalent to the innovation process in the usual situation where the observation noise is a Brownian motion -- is introduced. Zakai's approach is partly extended to derive filtering equations when the signal process is a diffusion. The case of conditionally Gaussian linear systems is analyzed. Closed form equations are derived both for the mean of the optimal filter and the conditional variance of the filtering error. The results are explicit in various special cases