Manual Stochastic and Integral Geometry

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Stochastic Geometry |

Firstly, the intrinsic volumes of the excursion sets of a class of mixture models defined by the linear combination of Gaussian and t random fields, then for the skew-t random fields are derived analytically. They have been compared and tested on surfaces generated by simulations.

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In the second stage, these random fields have been applied to real surfaces measured from the UHMWPE component, involved in application of total hip implant, before and after wear simulation process. The primary results showed that the skew-t random field is more adequate, and flexible for modelling the topographic roughness.

Following these arguments, a statistical analysis approach, based on the skew-t random field, is then proposed.

Stochastic Geometry

Document type : Theses. Identifiers HAL Id : tel, version 1.

ISBN 13: 9783642097669

Citation Ola Ahmad. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes. Levertijd We doen er alles aan om dit artikel op tijd te bezorgen. Het is echter in een enkel geval mogelijk dat door omstandigheden de bezorging vertraagd is. Bezorgopties We bieden verschillende opties aan voor het bezorgen of ophalen van je bestelling. Welke opties voor jouw bestelling beschikbaar zijn, zie je bij het afronden van de bestelling.

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Scope of the Workshop

Auteur: Rolf Schneider Wolfgang Weil. Uitgever: Springer. Samenvatting Stochastic geometry deals with models for random geometric structures. Toon meer Toon minder. Schneider and W.

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Weil give priority to the basic concepts in stochastic geometry Each chapter section is concluded by notes in which the main references are cited and numerous possible extensions are discussed. After an introduction to random fields, the first part will focus on the construction of Gaussian random fields with prescribed invariance properties such as stationarity, self-similarity, or operator scaling property.

Sample paths properties such as modulus of continuity and Hausdorff dimension of graphs will be settled in the second part to understand links with fractal analysis.

Evaluating Definite Integrals Using Geometry

The third part will concern some methods of simulation and estimation for these random fields in a discrete setting. Some applications in medical imaging will be presented. Finally, the last part will be devoted to geometric constructions involving Marked Poisson Point Processes and shot noise processes.

The Gibbs point processes GPP constitute a large class of point processes with interaction between the points. The interaction can be attractive, repulsive, depending on geometrical features whereas the null interaction is associated with the so-called Poisson point process. Existence, uniqueness and non-uniqueness of GPP are non-trivial questions which we treat here with completely self-contained proofs.

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  • Finally we investigate the estimation of parameters. For sake of simplicity, during all the mini-course, we consider only the case of finite range interaction and the setting of marked points is not presented. Title Stochastic Geometry. Publisher Springer International Publishing. Print ISBN Electronic ISBN Editor: Prof. David Coupier.