Principles of Mathematical GeologyPreface 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. |
Contents
CHAPTER II | 29 |
4 | 46 |
5 | 58 |
6 | 90 |
7 | 109 |
1 | 149 |
4 | 183 |
References | 218 |
3 | 250 |
Reversibility | 272 |
CHAPTER V | 297 |
Statistical Inferences on Properties of Random | 347 |
Random Diffusion Processes | 387 |
Caming Problems and Paradigm of Geological | 429 |
| 439 | |
Probabilistic structures of Markov sequences | 226 |
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a₁ A₂ absolutely continuous axiom calculate called Cauchy distribution Chapter coefficients components conditional distribution conditional probability conformity corresponding critical region denoted density determined diffusion distribution function elementary events elements equal equation ergodic essentially non-Markov estimate example finite formula Geol geological events geologists given granite Hence homogeneous hypothesis independent random variables initial chain integral interval investigation large number Lebesgue integral Let us assume Let us consider lumping Markov order Markov property Markov transitions mathematical expectation mathematical geology matrix measure method Nauka normal distribution o-algebra observations one-dimensional P₁ packets parameters partial Markov plagioclase Poisson process probability space problem properties random sequence random vector realization Russian sample sequence of grains simple Markov chain stationary statistics stochastic stochastically independent subsets Theorem tion transformation transition probabilities values vector random variable Vistelius A.B. Xmax Εξ