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Chapter 1 Elementary Inequalities of Probabilities of Events |
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1 | (8) |
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1.1 Inclusion-exclusion Formula |
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1 | (1) |
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1.2 Corollaries of the Inclusion-exclusion Formula |
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2 | (1) |
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1.3 Further Consequences of the Inclusion-exclusion Formula |
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2 | (4) |
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1.4 Inequalities Related to Symmetric Difference |
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6 | (1) |
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1.5 Inequalities Related to Independent Events |
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6 | (2) |
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1.6 Lower Bound for Union (Chung-Erdos) |
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8 | (1) |
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8 | (1) |
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Chapter 2 Inequalities Related to Commonly Used Distributions |
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9 | (14) |
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2.1 Inequalities Related to the Normal d.f. |
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9 | (3) |
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2.2 Slepian Type Inequalities |
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12 | (5) |
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2.3 Anderson Type Inequalities |
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17 | (1) |
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2.4 Khatri-Sidak Type Inequalities |
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18 | (1) |
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2.5 Corner Probability of Normal Vector |
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19 | (1) |
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2.6 Normal Approximations of Binomial and Poisson Distributions |
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20 | (2) |
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22 | (1) |
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Chapter 3 Inequalities Related to Characteristic Functions |
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23 | (6) |
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3.1 Inequalities Related Only with c.f. |
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23 | (3) |
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3.2 Inequalities Related to c.f. and d.f. |
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26 | (1) |
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3.3 Normality Approximations of c.f. of Independent Sums |
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27 | (1) |
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28 | (1) |
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Chapter 4 Estimates of the Difference of Two Distribution Functions |
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29 | (8) |
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4.1 Fourier Transformation |
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29 | (4) |
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33 | (1) |
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4.3 Stieltjes Transformation |
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34 | (2) |
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36 | (1) |
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Chapter 5 Probability Inequalities of Random Variables |
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37 | (14) |
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5.1 Inequalities Related to Two r.v.'s |
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37 | (2) |
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5.2 Perturbation Inequality |
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39 | (1) |
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5.3 Symmetrization Inequalities |
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40 | (1) |
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41 | (1) |
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42 | (2) |
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5.6 Upper Bounds of Tail Probabilities of Partial Sums |
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44 | (1) |
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5.7 Lower Bounds of Tail Probabilities of Partial Sums |
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44 | (1) |
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5.8 Tail Probabilities for Maximum Partial Sums |
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45 | (1) |
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5.9 Tail Probabilities for Maximum Partial Sums (Continuation) |
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46 | (1) |
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5.10 Reflection Inequality of Tail Probability (Hoffmann-Jørgensen) |
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47 | (1) |
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5.11 Probability of Maximal Increment (Shao) |
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48 | (1) |
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5.12 Mogulskii Minimal Inequality |
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49 | (1) |
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50 | (1) |
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50 | (1) |
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Chapter 6 Bounds of Probabilities in Terms of Moments |
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51 | (16) |
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6.1 Chebyshev-Markov Type Inequalities |
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51 | (1) |
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52 | (1) |
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6.3 Series of Tail Probabilities |
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53 | (1) |
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6.4 Kolmogorov Type Inequalities |
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54 | (2) |
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6.5 Generalization of Kolmogorov Inequality for a Submartingale |
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56 | (1) |
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6.6 Renyi-Hajek Type Inequalities |
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57 | (3) |
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60 | (2) |
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6.8 Fuk and Nagaev Inequality |
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62 | (1) |
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6.9 Burkholder Inequality |
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63 | (2) |
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6.10 Complete Convergence of Partial Sums |
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65 | (1) |
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65 | (2) |
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Chapter 7 Exponential Type Estimates of Probabilities |
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67 | (17) |
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7.1 Equivalence of Exponential Estimates |
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67 | (1) |
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7.2 Petrov Exponential Inequalities |
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68 | (2) |
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70 | (2) |
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72 | (1) |
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73 | (1) |
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7.6 Exponential Bounds for Sums of Bounded Variables |
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74 | (1) |
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7.7 Kolmogorov Inequalities |
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75 | (4) |
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79 | (1) |
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7.9 Exponential Inequalities by Censoring |
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80 | (2) |
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7.10 Tail Probability of Weighted Sums |
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82 | (1) |
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83 | (1) |
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Chapter 8 Moment Inequalities Related to One or Two Variables |
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84 | (13) |
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8.1 Moments of Truncation |
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84 | (1) |
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8.2 Exponential Moment of Bounded Variables |
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84 | (1) |
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8.3 Holder Type Inequalities |
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85 | (1) |
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8.4 Jensen Type Inequalities |
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86 | (1) |
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8.5 Dispersion Inequality of Censored Variables |
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87 | (1) |
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8.6 Monotonicity of Moments of Sums |
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88 | (1) |
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8.7 Symmetrization Moment Inequatilies |
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88 | (1) |
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89 | (1) |
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8.9 Exponential Moment of Normal Variable |
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90 | (3) |
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8.10 Inequatilies of Nonnegative Variable |
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93 | (1) |
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94 | (1) |
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8.12 Exponential Moment of Upper Truncated Variables |
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95 | (1) |
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96 | (1) |
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Chapter 9 Moment Estimates of (Maximum of) Sums of Random Variables |
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97 | (33) |
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9.1 Elementary Inequalities |
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97 | (2) |
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9.2 Minkowski Type Inequalities |
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99 | (1) |
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100 | (1) |
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101 | (4) |
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105 | (1) |
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9.6 Khintchine Inequality |
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106 | (2) |
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9.7 Marcinkiewicz-Zygmund-Burkholder Type Inequalities |
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108 | (3) |
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9.8 Skorokhod Inequalities |
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111 | (1) |
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9.9 Moments of Weighted Sums |
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112 | (1) |
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9.10 Doob Crossing Inequalities |
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113 | (1) |
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9.11 Moments of Maximal Partial Sums |
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114 | (1) |
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115 | (2) |
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9.13 Equivalence Conditions for Moments |
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117 | (6) |
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9.14 Serfling Inequalities |
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123 | (4) |
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127 | (1) |
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128 | (2) |
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Chapter 10 Inequalities Related to Mixing Sequences |
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130 | (19) |
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10.1 Covariance Estimates for Mixing Sequences |
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131 | (3) |
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10.2 Tail Probability on α-mixing Sequence |
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134 | (1) |
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10.3 Estimates of 4-th Moment on ρ-mixing Sequence |
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135 | (1) |
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10.4 Estimates of Variances of Increments of ρ-mixing Sequence |
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136 | (2) |
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10.5 Bounds of 2 + δ-th Moments of Increments of ρ-mixing Sequence |
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138 | (2) |
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10.6 Tail Probability on φ-mixing Sequence |
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140 | (2) |
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10.7 Bounds of 2 + δ-th Moment of Increments of φ-mixing Sequence |
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142 | (1) |
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10.8 Exponential Estimates of Probability on φ-mixing Sequence |
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143 | (5) |
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148 | (1) |
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Chapter 11 Inequalities Related to Associative Variables |
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149 | (9) |
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11.1 Covariance of PQD Varaibles |
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149 | (1) |
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11.2 Probability of Quadrant on PA (NA) Sequence |
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150 | (1) |
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11.3 Estimates of c.f.'s on LPQD (LNQD) Sequence |
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151 | (1) |
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11.4 Maximal Partial Sums of PA Sequence |
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152 | (1) |
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11.5 Variance of Increment of LPQD Sequence |
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153 | (1) |
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11.6 Expectation of Convex Function of Sum of NA Sequence |
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154 | (2) |
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11.7 Marcinkiewicz-Zygmund-Burkholder Inequality for NA Sequence |
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156 | (1) |
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157 | (1) |
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Chapter 12 Inequalities about Stochastic Processes and Banach Space Valued Random Variables |
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158 | (22) |
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12.1 Probability Estimates of Supremums of a Wiener Process |
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158 | (4) |
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12.2 Probability Estimate of Supremum of a Poisson Process |
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162 | (2) |
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164 | (3) |
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167 | (1) |
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12.5 Tail Probability of Gaussian Process |
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168 | (1) |
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12.6 Tail Probability of Randomly Signed Independent Processes |
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168 | (2) |
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12.7 Tail Probability of Adaptive Process |
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170 | (2) |
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12.8 Tail Probability on Submartingale |
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172 | (1) |
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12.9 Tail Probability of Independent Sum in B-Space |
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173 | (1) |
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12.10 Isoperimetric Inequalities |
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173 | (1) |
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174 | (1) |
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12.12 Tail Probability of Normal Variable in B-Space |
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175 | (1) |
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12.13 Gaussian Measure on Symmetric Convex Sets |
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175 | (1) |
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12.14 Equivalence of Moments of B-Gaussian Variables |
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176 | (1) |
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12.15 Contraction Principle |
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176 | (2) |
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12.16 Symmetrization Inequalities in B-Space |
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178 | (1) |
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12.17 Decoupling Inequality |
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178 | (2) |
| References |
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180 | |
Lisainfo e-raamatute kohta