Ball throwing on spheres

Ball throwing on Euclidean spaces has been considered for a while. A suitable renormalization leads to a fractional Brownian motion as limit object. In this paper we investigate ball throwing on spheres. A different behavior is exhibited: we still get a Gaussian limit but which is no longer a fractional Brownian motion. However the limit is locally self-similar when the self-similarity index $H$ is less than 1/2

Estimation of the Hurst and the stability indices of a HH-self-similar stable process

In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at points $\frac{k}{n}$, $k=0,\ldots,n$. Our estimate is based on $\beta$-variations with $-\frac{1}{2}<\beta<0$. We obtain consistent estimators, with rate of convergence, for several classical $H$-sssi $\alpha$-stable processes (fractional Brownian motion, well-balanced linear fractional stable motion, Takenaka's processes, L\'evy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and L\'evy motion. Keywords: H-sssi processes; stable processes; self-similarity parameter estimator; stability parameter estimator

On Simulation of Manifold Indexed Fractional Gaussian Fields

To simulate fractional Brownian motion indexed by a manifold poses serious numerical problems: storage, computing time and choice of an appropriate grid. We propose an effective and fast method, valid not only for fractional Brownian fields indexed by a manifold, but for any Gaussian fields indexed by a manifold. The performance of our method is illustrated with different manifolds (sphere, hyperboloid).

On Simulation of Manifold Indexed Fractional Gaussian Fields

To simulate fractional Brownian motion indexed by a manifold poses serious numerical problems: storage, computing time and choice of an appropriate grid. We propose an effective and fast method, valid not only for fractional Brownian fields indexed by a manifold, but for any Gaussian fields indexed by a manifold. The performance of our method is illustrated with different manifolds (sphere, hyperboloid)

On Fractional Gaussian Random Fields Simulations

To simulate Gaussian fields poses serious numerical problems: storage and computing time. The midpoint displacement method is often used for simulating the fractional Brownian fields because it is fast. We propose an effective and fast method, valid not only for fractional Brownian fields, but for any Gaussian fields. First, our method is compared with midpoint for fractional Brownian fields. Second, the performance of our method is illustrated by simulating several Gaussian fields. The software FieldSim is an R package developed in R and C and that implements the procedures on which this paper focuses

Precision of systematic sampling and transitive methods

International audienceThe use of the transitive methods for assessing the precision of systematic sampling is discussed. A key point of the transitive methods is the choice of a local model for the covariogram near the origin. The relationship between the regularity of the measurements and the regularity of their covariogram is given. This result is useful for choosing the appropriate covariogram model. A method forestimating the measurement regularity from discrete data is proposed for cases where it cannot be assessed a priori. Stereological applications where sampling is based on geometric probes such as serial sections, point or line grids are also discussed

Experimentelle Bestimmung der gebundenen Wirbellinien sowie des Strömungsverlaufs in der Umgebung der Hinterkante eines schlanken Deltaflügels

Es wird über Grenzschichtmessungen an einem scharfkantigen schlanken Deltaflügel (Seitenverhältnis [Lambda] = 1,0, Anstellwinkel [alpha] = 20,5°) mit turbulenten Grenzschichten berichtet. Aus den Geschwindigkeiten am Rand der Grenzschicht auf Ober- und Unterseite ergibt sich der Verlauf der gebundenen Wirbellinien in der tragenden Fläche. Ein Vergleich mit früheren Untersuchungen bei laminaren Grenzschichten zeigt den Einfluß des Grenzschichtcharakters auf die Wirbelbildung. Untersuchungen über den Verlauf der Strömung stromabwärts von der Hinterkante lassen erkennen, daß sich die von der Hinterkante ausgehende Wirbelschceht zu einem Wirbel aufrollt, dessen Drehsinn dem des Vorderkantenwirbels entgegengesetzt ist. Die Achse dieses Hinterkantenwirbels verläuft spiralförmig um die Achse des Vorderkantenwirlwls