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Mass Transportation Problems, Volume II, Table of Contents

1998 Bild Mass Transportation Problems Vol. II Vorderseite Mass Transportation Problems
Vol. II: Applications
Coauthor: S. T. Rachev
Springer Verlag, 1998
Language: english

 
 
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