|
Contents to Volume II
|
| |
Preface to Volume II |
vii |
Preface to Volume I |
xi |
7 |
Relaxed or Additional Constraints |
1 |
| |
7.1 |
Mass Transportation Problem |
2 |
| |
7.2 |
Fixed Sum of the Marginals |
10 |
| |
7.3 |
Mass nansportation Problems
with Capacity Constraints |
17 |
| |
7.4 |
Local Bounds for the Uansportation Plans |
36 |
| |
7.5 |
Closeness of Measure
on a Finite Number of Directions |
42 |
| |
7.6 |
Moment Problems of Stochastic Processes
and Rounding Problems |
52 |
| |
7.6.1 |
Moment Problems and Kantorovich Radius |
54 |
| |
7.6.2 |
Moment Problems Related to Rounding Proportions |
57 |
| |
7.6.3 |
Closeness of Random Processes
with Fixed Moment Characteristics |
62 |
| |
7.6.4 |
Approximation of Queueing Systems
with Prescribed Moments |
71 |
| |
7.6.5 |
Rounding Random Numbers with Fixed Moments |
80 |
8 |
Probabilistic-Type Limit Theorems |
85 |
| |
8.1 |
Rate of Convergence in the CLT
with Respect to Kantorovich Metric |
85 |
| |
8.2 |
Application to Stable Limit Theorems |
102 |
| |
8.3 |
Summability Methods, Compound Poisson Approximation |
126 |
| |
8.4 |
Operator-Stable Limit Theorems |
131 |
| |
8.5 |
Proofs of the Rate of Convergence Results |
153 |
| |
8.6 |
Ideal Metrics in the Problem of Rounding |
178 |
9 |
Mass Uansportation Problems
and Recursive Stochastic Equations |
191 |
| |
9.1 |
Recursive Algorithms and Contraction
of Transformations |
191 |
| |
9.2 |
Convergence of Recursive Algorithms |
204 |
| |
9.2.1 |
Learning Algorithm |
204 |
| |
9.2.2 |
Branching-Type Recursion |
206 |
| |
9.2.3 |
Limiting Distribution of the Collision Resolution
Interval |
220 |
| |
9.2.4 |
Quicksort |
229 |
| |
9.2.5 |
Limiting Behavior of Random Maxima |
231 |
| |
9.2.6 |
Random Recursion Arising in Probabilistic Modeling:
Limit Laws |
236 |
| |
9.2.7 |
Random Recursion Arising in Probabilistic Modeling:
Rate of Convergence |
248 |
| |
9.3 |
Extensions of the Contraction Method |
254 |
| |
9.3.1 |
The Number of Inversions of a Random Permutation |
254 |
| |
9.3.2 |
The Number of Records |
257 |
| |
9.3.3 |
Unsuccessful Searching in Binary Search Trees |
260 |
| |
9.3.4 |
Successful Searching in Binary Search Trees |
263 |
| |
9.3.5 |
A Random Search Algorithm |
269 |
| |
9.3.6 |
Bucket Algorithm |
272 |
10 |
Stochastic Differential Equations
and Empirical Measures |
277 |
| |
10.1 |
Propagation of Chaos and Contraction
of Stochastic Mappings |
277 |
| |
10.1.1 |
Introduction |
277 |
| |
10.1.2 |
Equations with p-Norm Interacting Drifts |
279 |
| |
10.1.3 |
A Random Number of Particles |
290 |
| |
10.1.4 |
pth Mean Interactions in Time: A Non-Markovian Case |
293 |
| |
10.1.5 |
Minimal Mean Interactions in Time |
307 |
| |
10.1.6 |
Interactions with a Normalized Variation of the Neighbors:
Relaxed Lipschitz Conditions |
308 |
| |
10.2 |
Rates of Convergence
in the Kantorovich Metric |
322 |
| |
10.3 |
Stochastic Differential Equations |
332 |
References |
351 |
Abbreviations |
395 |
Symbols |
397 |
Index |
409 |
