Электронная книга: Dietrich Stoyan «Stochastic Geometry and Its Applications»

Stochastic Geometry and Its Applications

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.

Издательство: "John Wiley&Sons Limited"

ISBN: 9781118658246

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Dietrich Stoyan

Dietrich Stoyan

Dietrich Stoyan (born 1940, Germany) — mathematician, statistician; student of Mathematics at Technical University Dresden; applied research at Deutsches Brennstoffinstitut Freiberg, 1967 PhD, 1975 Habilitation. Since 1976 at TU Bergakademie Freiberg, President of that university in 1991—1997; he became famous by his statistical research of the diffusion of euro coins in Germany and Europe after the introduction of the euro in 2002.

Contents

Research

Queueing Theory

Qualitative theory, in particular inequalities, for queueing systems and related stochastic models. The books

  • D. Stoyan: Comparison Methods for Queues and other Stochastic Models. J. Wiley and Sons, Chichester, 1983 and
  • A. Mueller and D. Stoyan: Comparison Methods for Stochastic Models and Risks, J. Wiley and Sons, Chichester, 2002

report on the results. The work goes back to 1969 when he discovered the monotonicity of the GI/G/1 waiting times with respect to the convex order.

Stochastic Geometry

Stereological formulae, applications for marked point process, development of stochastic models. Successful joint work with Joseph Mecke led to the first exact proof of the fundamental stereological formulae.

The book Stochastic Geometry and its Applications, by D. Stoyan, W.S. Kendall and J. Mecke reports on the results. The book of 1995 is the key reference for applied stochastic geometry.

Spatial Statistics

Statistical methods for point processes, random sets and many other random geometrical structures such as fibre processes. Results can be found in the 1995 book on stochastic geometry and in the book, Fractals, Random Shapes and Point Fields by D. and H. Stoyan. (J. Wiley and Sons, Chichester, 1994).

A particular strength of Stoyan are second-order methods.

At the moment Dietrich Stoyan is working (together with three colleagues) for a new book on point process statistics. He used packings of hard spheres as models for materials with the aim to solve mechanical problems for random heterogeneous materials.

Stoyan is very active in demonstrating non-mathematicians and non-statisticians the potential of statistical and stochastic geometrical methods. In particular, he coorganized together with Klaus Mecke conferences where physicists, geometers and statisticians met. See the books

  • Mecke Klaus R. and Stoyan D. (eds.): Statistical Physics and Spatial Statistics. Lecture Notes in Physics 554, Springer-Verlag, 2000 and
  • Mecke Klaus R. and Stoyan D. (eds.): Morphology of Condensed Matter. Lecture Notes in Physics 600, Springer-Verlag, 2002.

See also

  • Freiberg
  • Freiberg University of Mining and Technology
  • Stochastic geometry

External links

Источник: Dietrich Stoyan

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