1. Probability and Random Variables: A Short Résumé.- 1.1 Basic Concepts.- 1.2 Some Probability Distributions.- 1.3 Convergence of Sequences of Random Variables.- 1.4 Stochastic Processes.- 2. Continuous Random Fields.- 2.1 Basic Concepts.- 2.2 Homogeneous Random Fields.- 2.3 Isotropic Random Fields.- 2.4 Locally Homogeneous and Isotropic Random Fields.- 2.5 Space-Time Random Fields.- 2.6 Vector-Valued Random Fields.- 2.7 Tensor-Valued Random Fields.- 2.8 Markov Random Fields.- 2.9 Fields Governed by Stochastic Equations.- 3. Random Point Fields.- 3.1 Basic Properties.- 3.2 Poisson Random Fields.- 3.3 Boolean Random Fields.- 3.4 Markov and Gibbs Fields.- 3.5 Random Configurations of Objects.- 3.6 Random Set Patterns.- 4. Statistical Inference.- 4.1 Introductory Remarks.- 4.2 Estimation of Mean and Covariance.- 4.3 Estimation of Spectral Density.- 4.4 Prediction Problems: Kriging.- 4.5 Spatial Sampling Design.- 4.6 Inference for Point Fields.- 4.7 Stereology.- 4.8 Simulation and Remarks.- 5. Material Media Microstructure: Modeling Issues.- 5.1 Basic Characteristics of Microstructure.- 5.2 Averaging Procedures.- 5.3 Homogenization and Smoothing.- 5.4 Random Porous Media.- 5.5 Spatial Randomness in Solid Materials.- 6. Physical Phenomena in Random Microstructures: Selected Applications.- 6.1 Introductory Remarks.- 6.2 Wave Propagation.- 6.3 Pollution Transport in Groundwater.- 6.4 Deformation of Random Elastic Materials.- 6.5 Random Microstructure and Fracture.- 6.6 Other Problems and Remarks.- References.- Author Index.

This book is for a general scientific and engineering audience as a guide to current ideas, methods, and models for stochastic modeling of microstructures.

It is a reference for professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.