Mass transportation problems: 1 Theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Probability and its applications series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 508 S. |
| ISBN: | 0387983503 |
Staff View
MARC
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| 100 | 1 | |a Račev, Svetlozar T. |d 1951- |e Verfasser |0 (DE-588)12022979X |4 aut | |
| 245 | 1 | 0 | |a Mass transportation problems |n 1 |p Theory |c Svetlozar T. Rachev ; Ludger Rüschendorf |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XXV, 508 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Probability and its applications series | |
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Record in the Search Index
| _version_ | 1804126540991037440 |
|---|---|
| adam_text | Contents
to
Volume
I
Preface to Volume I
vii
Preface to Volume II
xv
1
Introduction
χ
1.1
Mass Transportation Problems in Probability Theory
... 1
1.2
Specially Structured Transportation Problems
....... 21
1.3
Two Examples of the Interplay Between Continuous
and Discrete MTPs
...................... 23
1.4
Stochastic Applications
.................... 27
2
The Monge-Kantorovich Problem
57
2.1
The Multivariate Monge-Kantorovich Problem:
An Introduction
........................ 58
2.2
Primal and Dual Monge-Kantorovich Functionals
..... 64
2.3
Duality Theorems in a Topological Setting
......... 76
2.4
General Duality Theorem
.................. 82
2.5
Duality Theorems with Metric Cost F inctions
....... 86
2.6
Dual Representation for bp-Minimal Metrics
........ 96
xx Contents
to
Volume
I
3
Explicit Results for the Monge-Kantorovich Problem
107
3.1
The One-Dimensional Case
................. 107
3.2
The Convex Case
....................... 112
3.3
The General Case
....................... 123
3.4
An Extension of the Kantorovich I^-Minimal Problem
. . 132
3.5
Maximum Probability of Sets, Maximum of Sums,
and Stochastic Order
..................... 144
3.6
Hoeffding-Fréchet
Bounds
.................. 151
3.7
Bounds for the Total Transportation Cost
......... 158
4
Duality Theory for Mass Transfer Problems
161
4.1
Duality in the Compact Case
................ 161
4.2
Cost Functions with Triangle Inequality
.......... 172
4.3
Reduction Theorems
..................... 190
4.4
Proofs of the Main Duality Theorems and a Discussion
. . 207
4.5
Duality Theorems for Noncompact Spaces
......... 219
4.6
Infinite Linear Programs
................... 241
4.6.1
Duality Theory for an Abstract Scheme
of Infinite-Dimensional Linear Programs
and Its Application to the Mass Transfer Problem
.... 241
4.6.2
Duality Theorems for the Mass Transfer Problem
with Given Marginals
..................... 245
4.6.3
Duality Theorem for a Marginal Problem
with Additional Constraints of Moment-Type
....... 251
4.6.4
Duality theorem for a Further Extremal
Marginal Problem
....................... 258
4.6.5
Duality Theorem for a Nontopological Version
of the Mass Transfer Problem
................ 265
5
Applications of the Duality Theory
275
5.1
Mass Transfer Problem with a Smooth
Cost Function—Explicit Solution
.............. 275
5.2
Extension and Approximate Extension Theorems
..... 290
5.2.1
The Simplest Extension Theorem
(the Case X
=
E(S) and
Χχ
=
E(Si))
........... 290
5.2.2
Approximate Extension Theorems
............. 292
5.2.3
Extension Theorems
..................... 295
Contents
to
Volume
I
xxi
5.2.4
A continuous selection theorem
............... 302
5.3
Approximation Theorems
.................. 306
5.4
An Application of the Duality Theory
to the Strassen Theorem
................... 319
5.5
Closed Preorders and Continuous Utility Functions
.... 322
5.5.1
Statement of the Problem and the Idea
of the Duality Approach
................... 322
5.5.2
Functionally Closed Preorders
................ 324
5.5.3
Two Generalizations of the Debreu Theorem
........ 329
5.5.4
The Case of a Locally Compact Space
........... 335
5.5.5
Varying preorders and a universal utility theorem
.... 337
5.5.6
Functionally Closed Preorders
and Strong Stochastic Dominance
.............. 341
5.6
Further Applications to Utility Theory
........... 344
5.6.1
Preferences That Admit Lipschitz
or Continuous Utility Functions
............... 344
5.6.2
Application to Choice Theory
in Mathematical Economics
................. 352
5.7
Applications to Set-Valued Dynamical Systems
...... 354
5.7.1
Compact-Valued Dynamical Systems:
Quasiperiodic Points
..................... 354
5.7.2
Compact-Valued Dynamical Systems:
Asymptotic Behavior of Trajectories
............ 358
5.7.3
A Dynamic Optimization Problem
............. 363
5.8
Compensatory Transfers and Action Profiles
........ 367
6
Mass Transshipment Problems and Ideal Metrics
371
6.1
Kantorovich-Rubinstein Problems with Constraints
.... 372
6.2
Constraints on the /cth Difference of Marginals
...... 383
6.3
The General Case
....................... 402
6.4
Minimality of Ideal Metrics
................. 414
References
429
Abbreviations
473
Symbols
475
Index
487
|
| any_adam_object | 1 |
| author | Račev, Svetlozar T. 1951- Rüschendorf, Ludger 1948- |
| author_GND | (DE-588)12022979X (DE-588)10867472X |
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| author_role | aut aut |
| author_sort | Račev, Svetlozar T. 1951- |
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| dewey-full | 519.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/2 |
| dewey-search | 519.7/2 |
| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV011953292 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:19:05Z |
| institution | BVB |
| isbn | 0387983503 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008081681 |
| oclc_num | 174815204 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-20 DE-703 DE-384 DE-824 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-521 DE-355 DE-BY-UBR DE-634 DE-11 |
| physical | XXV, 508 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications series |
| spelling | Račev, Svetlozar T. 1951- Verfasser (DE-588)12022979X aut Mass transportation problems 1 Theory Svetlozar T. Rachev ; Ludger Rüschendorf New York [u.a.] Springer 1998 XXV, 508 S. txt rdacontent n rdamedia nc rdacarrier Probability and its applications series Transportproblem (DE-588)4060694-6 gnd rswk-swf Transportproblem (DE-588)4060694-6 s DE-604 Rüschendorf, Ludger 1948- Verfasser (DE-588)10867472X aut (DE-604)BV011953286 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Račev, Svetlozar T. 1951- Rüschendorf, Ludger 1948- Mass transportation problems Transportproblem (DE-588)4060694-6 gnd |
| subject_GND | (DE-588)4060694-6 |
| title | Mass transportation problems |
| title_auth | Mass transportation problems |
| title_exact_search | Mass transportation problems |
| title_full | Mass transportation problems 1 Theory Svetlozar T. Rachev ; Ludger Rüschendorf |
| title_fullStr | Mass transportation problems 1 Theory Svetlozar T. Rachev ; Ludger Rüschendorf |
| title_full_unstemmed | Mass transportation problems 1 Theory Svetlozar T. Rachev ; Ludger Rüschendorf |
| title_short | Mass transportation problems |
| title_sort | mass transportation problems theory |
| topic | Transportproblem (DE-588)4060694-6 gnd |
| topic_facet | Transportproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011953286 |
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