| Description |
1 online resource (xv, 523 pages) : illustrations |
| Series |
De Gruyter studies in mathematics ; 23 |
|
De Gruyter studies in mathematics ; 23.
|
| Contents |
23 Uniqueness and Continuity Theorems24 Normal distribution and independence; 25 Differentiability of Fourier transforms; 26 Continuous mappings into the circle; Chapter VI Limit Distributions; 27 Examples of limit theorems; 28 The Central Limit Theorem; 29 Infinitely divisible distributions; 30 Gauss measures and multi-dimensional central limit theorem; Chapter VII Law of the Iterated Logarithm; 31 Posing the question and elementary preparations; 32 Probabilistic preparations; 33 Strassen's theorem of the iterated logarithm; 34 Supplements |
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49 Optional times and optional sampling50 The strong Markov property; 51 Prospectus; Bibliography; Symbol Index; Name Index; General Index |
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9 Infinite products of probability spacesChapter III Laws of Large Numbers; 10 Posing the question; 11 Zero-one laws; 12 Strong Law of Large Numbers; 13 Applications; 14 Almost sure convergence of infinite series; Chapter IV Martingales; 15 Conditional expectations; 16 Martingales -- definition and examples; 17 Transformation via optional times; 18 Inequalities for supermartingales; 19 Convergence theorems; 20 Applications; Chapter V Fourier Analysis; 21 Integration of complex-valued functions; 22 Fourier transformation and characteristic functions |
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Chapter VIII Construction of Stochastic Processes35 Projective limits of probability measures; 36 Kernels and semigroups of kernels; 37 Processes with stationary and independent increments; 38 Processes with pre-assigned path-set; 39 Continuous modifications; 40 Brownian motion as a stochastic process; 41 Poisson processes; 42 Markov processes; 43 Gauss processes; 44 Conditional distributions; Chapter IX Brownian Motion; 45 Brownian motion with filtration and martingales; 46 Maximal inequalities for martingales; 47 Behavior of Brownian paths; 48 Examples of stochastic integrals |
| Bibliography |
Includes bibliographical references (pages 493-500) and indexes |
| Notes |
English |
| Subject |
Probabilities.
|
|
probability.
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MATHEMATICS -- Probability & Statistics -- General.
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Probabilities
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| Form |
Electronic book
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| Author |
Burckel, Robert B
|
| LC no. |
95039173 |
| ISBN |
9783110814668 |
|
3110814668 |
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