| Preface |
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vii | |
| Acronyms |
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ix | |
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1 Strong Laws and Large Deviations |
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1 | (26) |
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1.1 Strong Limit Theorems of Probability Theory: Results, Problems and Methods |
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1 | (14) |
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1.2 The Universal Strong Laws and the Large Deviations Method |
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15 | (12) |
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2 Large Deviations for Sums of Independent Random Variables |
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27 | (50) |
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2.1 Probabilities of Large Deviations |
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27 | (1) |
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2.2 The Method of Conjugate Distributions |
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28 | (3) |
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2.3 Completely Asymmetric Stable Laws with Exponent α > 1 |
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31 | (2) |
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2.4 Functions of Large Deviations Theory and a Classification of Probability Distributions |
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33 | (4) |
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2.5 Large Deviations and a Non-Invariance |
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37 | (1) |
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2.6 Methods of Conjugate Distributions and Truncations |
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38 | (3) |
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2.7 Asymptotic Expansions of Functions of Large Deviations Theory in Case of Finite Variations |
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41 | (5) |
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2.8 Large Deviations in Case of Finite Variations |
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46 | (6) |
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2.9 Asymptotic Expansions of Functions of Large Deviations Theory for D(2) |
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52 | (4) |
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2.10 Asymptotic Expansions of Functions of Large Deviations Theory for DN(α) and D(α) |
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56 | (5) |
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2.11 Large Deviations for D(2) |
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61 | (7) |
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2.12 Large Deviations for DN(α) and D(α) |
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68 | (3) |
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2.13 Large Deviations and the Classification of Distributions |
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71 | (4) |
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2.14 Bibliographical Notes |
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75 | (2) |
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3 Strong Limit Theorems for Sums of Independent Random Variables |
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77 | (42) |
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3.1 Norming Sequences in Strong Limit Theorems |
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77 | (2) |
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3.2 Universal Strong Laws in Case of Finite Exponential Moments |
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79 | (5) |
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3.3 Universal Strong Laws for Random Variables without Exponential Moment |
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84 | (3) |
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3.4 Corollaries of the Universal Strong Laws |
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87 | (18) |
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3.4.1 The Erdos-Renyi and Shepp Laws |
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88 | (1) |
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3.4.2 The Csorgo-Revesz Laws |
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89 | (9) |
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3.4.3 The Law of the Iterated Logarithm |
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98 | (3) |
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3.4.4 The Strong Law of Large Numbers |
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101 | (2) |
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3.4.5 Results for Moduli of Increments of Sums of Independent Random Variables |
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103 | (2) |
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3.5 Optimality of Moment Assumptions |
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105 | (6) |
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3.6 Necessary and Sufficient Conditions for the Csorgo-Revesz Laws |
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111 | (4) |
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3.7 Bibliographical Notes |
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115 | (4) |
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4 Strong Limit Theorems for Processes with Independent Increments |
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119 | (18) |
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4.1 The Universal Strong Laws for Processes with Independent Increments |
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119 | (7) |
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4.2 Strong Laws for Increments of Wiener and Stable Processes without Positive Jumps |
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126 | (1) |
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4.3 Applications of the Universal Strong Laws |
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127 | (6) |
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4.4 Compound Poisson Processes |
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133 | (2) |
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4.5 Bibliographical Notes |
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135 | (2) |
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5 Strong Limit Theorems for Renewal Processes |
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137 | (16) |
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5.1 The universal Strong Laws for Renewal Processes |
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137 | (9) |
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5.2 Corollaries of the Universal Strong Laws |
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146 | (5) |
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5.3 Bibliographical Notes |
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151 | (2) |
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6 Increments of Sums of Independent Random Variables over Head Runs and Monotone Blocks |
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153 | (22) |
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6.1 Head Runs and Monotone Blocks |
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153 | (2) |
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6.2 Increments of Sums over Head Runs and Monotone Blocks |
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155 | (2) |
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6.3 The Universal Strong Laws |
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157 | (11) |
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6.4 Corollaries of the Universal Strong Laws |
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168 | (6) |
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6.5 Bibliographical Notes |
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174 | (1) |
| Bibliography |
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175 | (10) |
| Author Index |
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185 | (2) |
| General Index |
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187 | |
