Principles of Mathematical Geology, Softcover reprint of the original 1st ed. 1992

Preface to the English edition xiii Basic notations xv Introduction xvii amPl'ER 1. Mathenatical Geology and the Developnent of Geological Sciences 1 1. 1 Introduction 1 1. 2 Developnent of geology and the change of paradigms 2 1. 3 Organization of the mediun and typical structures 8 1. 4 statement of the problem: the role of models in the search for solutions 14 1. 5 Mathematical geology and its developnent 19 References 23 amPTER II. Probability Space and Randan Variables 29 11. 1 Introduction 29 11. 2 Discrete space of elementary events 29 11. 2. 1 Probability space 30 II. 2 ? 2 Randan variabl es 33 11. 3 Kolroogorov's axian; The Lebesgue integral 35 II. 3. 1 Probability space and randan variables 36 I 1. 3. 2 The Lebesgue integral 40 II. 3. 3 Nunerical characteristics of raman variables 44 II. 4 ~les of distributions of randan variables 46 II. 4. 1 Discrete distributions 46 II. 4. 2 Absolutely continuous distributions 51 II. 5 Vector randan variables 58 II. 5. 1 Product of probability spaces 58 II. 5. 2 Distribution of vector randan variables 60 II. 5. 3 Olaracteristics of vector randan variables 65 11. 5. 4 Exanples of distributions of vector raman variabl es 69 II . 5. 5 Conditional distributions with respect to randan variables 81 II. 6 Transfomations of randan variables 90 11. 6. 1 Linear transfomations 91 II. 6. 2 Sane non-linear transfomations 95 11. 6.

I. Mathematical Geology and the Development of Geological Sciences.- I.1 Introduction.- I.2 Development of geology and the change of paradigms.- I.3 Organization of the medium and typical structures.- I.4 Statement of the problem: the role of models in the search for solutions.- I.5 Mathematical geology and its development.- References.- II. Probability Space and Random Variables.- II. 1 Introduction.- II.2 Discrete space of elementary events.- II.3 Kolmogorov’s axiom; The Lebesgue integral.- II.4 Exanples of distributions of random variables.- II.5 Vector random variables.- II.6 Transformations of random variables.- II.7 Sequences of independent random variables and limit theorems.- II.8 Random processes and geometric probabilities.- References.- III. Basic Statistical Concepts — Problems of Estimation and Testing of Hypotheses.- III.1 Introductory remarks.- III.2 Point estimation.- III.3 Testing of statistical hypotheses.- III.4 On confidence intervals.- III.5 On robustness.- References.- IV. Randan Sequences and their Markov Chains.- IV. 1 Introduction.- IV.2 Probabilistic structures of Markov sequences.- IV.3 Matrix methods in the study of Markov chains.- IV. 4 Some generalizations of the Markov property.- IV. 5 Three-dimensional packing and Markov sequences.- References.- V. Transformations of Markov chains.- V. 1 Introduction.- V.2 Lumping over a set of states.- V.3 Concentration and rarefaction.- V.5 Sequences of packets.- References.- VI. Statistical Inferences on Properties of Randan Sequences and Markov Hypotheses.- VI. 1 Introduction.- VI. 2 Test of homogeneity.- VI.3 Test of reversibility.- VI.4 Likelihood ratio criterion ? for testing proportionality of transition probabilities.- VI.5 Markov hypotheses.- VI. 6 Partial Markov.- VI.7 Experimental checkof consistency of statistical tests on Markov order.- References.- VII. Randan Diffusion Processes.- VII. 1 Introduction.- VII.2 The general model.- VII.3 Particular models of diffusion.- References.- VIII. Coming Problems and Paradigm of Geological Sciences of the 21st Century.- VIII.1 Introduction.- VIII.2 Time and Compositional data.- VIII.3 Models.- References.- Authors Index.- Geographical Index.