Principles of Mathematical Geology

1. Front Matter

   Pages i-xxi

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2. Mathematical Geology and the Development of Geological Sciences

   • A. B. Vistelius

   Pages 1-27

3. Probability Space and Random Variables

   • A. B. Vistelius

   Pages 29-147

4. Basic Statistical Concepts — Problems of Estimation and Testing of Hypotheses

   • A. B. Vistelius

   Pages 149-219

5. Random Sequences and their Markov Chains

   • A. B. Vistelius

   Pages 221-296

6. Transformations of Markov Chains

   • A. B. Vistelius

   Pages 297-346

7. Statistical Inferences on Properties of Random Sequences and Markov Hypotheses

   • A. B. Vistelius

   Pages 347-386

8. Random Diffusion Processes

   • A. B. Vistelius

   Pages 387-428

9. Coming Problems and Paradigm of Geological Sciences of the 21st Century

   • A. B. Vistelius

   Pages 429-437

10. Back Matter

    Pages 439-477

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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.

• Hypothese
• Markov chain
• Markov process
• diffusion process
• digital elevation model
• probability space

` The most outstanding feature of this book is the clear, rigorous, and comprehensive presentation of Vistelius' concept of what mathematical geology is and where it should be heading in the future. It summarizes more than fifty years of experience, work, and understanding. ... this book should be mandatory reading for all those interested and working in mathematical geology because it presents much food for thought. '
Mathematical Geology, 26:3 (1994)

• Laboratory of Mathematical Geology, St. Petersburg, Russia

  A. B. Vistelius

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