Probabilistic Inequalities

Contents......Page 10
Preface......Page 8
1. Introduction......Page 14
2.1 Introduction......Page 16
2.2 One Dimensional Results......Page 17
2.3 Multidimensional Results......Page 20
2.4 Applications......Page 23
2.5 Addendum......Page 25
3.1 Introduction......Page 28
3.2 Results......Page 29
3.3 Application to Probability Theory......Page 42
4.2 Make Applications......Page 44
4.3 Remarks on an Inequality......Page 48
4.4 Lq; q > 1, Related Theory......Page 49
5.1 Introduction......Page 52
5.2 Main Results......Page 53
6.1 Background......Page 58
6.2 Main Results......Page 59
7.1 Background......Page 68
7.2 All Results......Page 69
8.1 Background......Page 86
8.2 Results Based on Taylor\'s Formula......Page 87
8.3 Results Based on Generalized Taylor{Widder Formula......Page 97
8.4 Results Based on an Alternative Expansion Formula......Page 105
9.1 Background......Page 114
9.2 Results......Page 115
10.1 Background......Page 130
10.2 Results......Page 132
11.1 Background......Page 148
11.2 Results......Page 150
12.1 Background......Page 168
12.2 Results......Page 169
13.1 Background......Page 174
13.2 Main Results......Page 177
14.1 Introduction......Page 186
14.2 Background......Page 187
14.3 Main Results......Page 189
15.1 Introduction......Page 206
15.2 Main Results......Page 207
16.1 The Standard Moment Problem......Page 228
16.2 The Convex Moment Problem......Page 233
16.3 Infinite Many Conditions Moment Problem......Page 237
16.4 Applications – Discussion......Page 239
17.1 Preliminaries......Page 240
17.2 Results......Page 241
18.1 Preliminaries......Page 252
18.2 Bounds for Random Rounding Rules......Page 253
18.3 Comparison of Bounds for Random and Deterministic Rounding Rules......Page 257
19.1 Preliminaries......Page 262
19.2 Results......Page 264
19.3 Proofs......Page 270
20.1 Introduction and Main Result......Page 276
20.2 Auxiliary Moment Problem......Page 278
20.3 Proof of Theorem 20.1.......Page 280
20.4 Concluding Remarks......Page 281
21.1 Main Result......Page 282
21.2 Outline of Proof......Page 286
22.1 Main Result......Page 290
22.2 An Auxiliary Moment Problem......Page 295
22.3 Further Auxiliary Results......Page 301
22.4 Minimizing Solutions in Boxes......Page 304
22.5 Conclusions......Page 309
23.1 Introduction......Page 314
23.2 Preliminaries......Page 315
23.3 Main Results......Page 318
23.3.1. The Financial Portfolio Problem......Page 322
23.3.2. The Portfolio Problem Involving Three Securities (similarly one can treat the problem of more than three securities).......Page 325
23.3.3. Applications of -Moment Problem to Variance......Page 329
23.3.4. The Multivariate Case......Page 341
24.2 Results......Page 344
25.2 Main Results......Page 358
25.3 Applications......Page 365
26.1 Background......Page 368
26.2 Main Results......Page 369
26.3 Applications......Page 381
27.1 Results......Page 386
27.2 Applications......Page 390
28.1 Results......Page 392
Bibliography......Page 408
List of Symbols......Page 426
Index......Page 428