Author | Beneลก, Viktor. author |
---|---|

Title | Stochastic Geometry: Selected Topics [electronic resource] / by Viktor Beneลก, Jan Rataj |

Imprint | Boston, MA : Springer US, 2004 |

Connect to | http://dx.doi.org/10.1007/b129604 |

Descript | XI, 221 p. online resource |

SUMMARY

Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand

CONTENT

Preliminaries -- Random Measures and Point Processes -- Random Fibre and Surface Systems -- Vertical Sampling Schemes -- Fibre and Surface Anisotropy -- Particle Systems

Mathematics
Measure theory
Convex geometry
Discrete geometry
Probabilities
Statistics
Materials science
Mathematics
Probability Theory and Stochastic Processes
Statistics general
Convex and Discrete Geometry
Measure and Integration
Characterization and Evaluation of Materials