Comparison methods for stochastic models and risks:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2002
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 330 S. Ill., graph. Darst. |
| ISBN: | 0471494461 9780471494461 |
Internformat
MARC
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| 245 | 1 | 0 | |a Comparison methods for stochastic models and risks |c Alfred Müller ; Dietrich Stoyan |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2002 | |
| 300 | |a XII, 330 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Systèmes stochastiques | |
| 650 | 4 | |a Stochastic systems | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009644092 | ||
Datensatz im Suchindex
| _version_ | 1804128944281092096 |
|---|---|
| adam_text | Contents
Preface
.................................... ix
1 Uiiivariate
Stochastic
Orders ................... 1
1.1
Introduction
............................. 1
1.2
Usual Stochastic· Order
....................... 2
1.3
Hazard Rate Order
......................... 8
1.4
Likelihood Ratio Order
...................... 12
1.5
Convex Orders
........................... 15
l.ő.l
Fundamental Properties
.................. 15
1.5.2
Sufficient Conditions and Strassen s Theorem
...... 23
1.3.3
Majorization
........................ 31
l.C Higher Convexity Orders and Laplace Transform Order
.... 37
1.7
Dispersive Order and Relative Inverse Function
Orderings
... 40
1.8
Lifetime Distributions and Notions of Aging
........... 45
1.9
Bivariate Characterizations
.................... 51
1.10
Extremal Elements
......................... 55
1.11
Monotone Approximations
..................... 59
1.12
Relationships and Comparison Criteria for Univariate Stochas¬
tic Orders
..............................
GO
2
Theory of Integral Stochastic Orders
..............
Go
2.1
Introduction
.............................
G5
2.2
Tools from Functional Analysis
..................
G7
2.3
Maximal Generators of Integral Stochastic Orders
.......
G9
2.4
Properties of Stochastic Orders
.................. 73
2.5
Small Generators
.......................... 75
2.
G
Sf
rassen
Type Theorems
......................
-Si)
3
Multivariate Stochastic Orders
.................. 85
3.1
Preliminaries
............................ 85
3.2
Properties of Mulrivariate Stochastic Orders
........... 89
3.3
Usual Stochastic Order and Orthant Orders
........... 90
vi
CONTEXTS
3.4
Convex Orders
........................... 98
3.ő
Linear Convex Orders
....................... 101
3.C Componentwise Convex Order
.................. 103
3.7
Stochastic Orders Defined by Difference Operators
....... 105
3.8
Dependence Orders
......................... 107
3.9
Supenuodular Order
........................ 112
3.10
Concepts of Dependence
...................... 121
3.11
Multivariate Likelihood Ratio Orders
............... 129
3.12
Directionally Convex Order
.................... 131
3.13
Stochastic Ordering of Multivariate Normal Distributions
. . . 141
3.14
Relationships and Comparison Criteria for Multivariate
Stochastic Orders
.......................... 145
4
Stochastic Models, Comparison and
Monotonicity
...... 149
4.1
General Considerations Concerning Stochastic Models
..... 149
4.2
Monotonicity
aud
Comparability
................. 154
4.2.1
Monotonicity
........................
154
4.2.2
Comparability
....................... 154
4.3
Methods for Establishing
Monotonicity
and Comparability
Properties
.............................. 155
4.3.1
The Functional Method
.................. 155
4.3.2
The Mapping Method
................... 156
4.3.3
The Coupling Method
................... 166
4.4
Extremal Problems
......................... 171
5
Monotonicity
and Comparability of Stochastic Processes
. . 173
•j.l Introduction
............................. 173
5.2
Comparability and Monotonieity of Markov Processes
..... 180
5.2.1
Monotone and Comparable Operators
.......... 180
•5.2.2
Monotonicity and Comparability Conditions for Markov
Processes
.......................... 185
5.2.3
Homogeneous Markov Processes with
Discret«4
State Space
192
5.2.4
Monotonicity Properties of Second Order Characteris¬
tics of Markov Chains
................... 198
5.2.5
Application of Monotone Markov Chains: Perfect
Simulation
......................... 201
5.2.6
Markov Decision Processes
................ 204
5.3
Monotonieity and Comparability of Non-Markov Processes
. . . 207
5.4
Comparison of Point Processes
.................. 211
6
Monotonicity Properties and Bounds for Queueing Systems
217
G.I Basic Facts for GI/GI/l and G/G/l
...............217
G.2 Monotonicity Properties of GI/GI/l and G/G/l Queues
.... 220
6.3
Comparison Properties of GI/GI/l and G/G/l
.........221
CONTEXTS
Vil
6.4
Bounds Obtained from Comparison Properties of GI/GI/l
. . . 225
6.5
Bounds in the Case of Non-renewal Input
............ 226
6.6
Basic Facts for the Multi-server System GI/GI/s
........ 228
6.7
Monotonicity Properties of GI/GI/s Queues
........... 229
6.8
Comparability Properties of GI/GI/s
............... 231
6.9
Remarks on other Queueiug Systems
............... 235
7
Applications to Various Stochastic Models
...........237
7.1
Monotonicity Properties and Bounds for the Renewal Function
237
7.2
Reliability Applications
......................239
7.2.1
Coherent Systems
.....................239
7.2.2
Comparison of Maintenance Policies
...........242
7.3
PERT and Scheduling Problems
.................244
7.4
Comparison of Random Sets and Point Processes
........247
7.4.1
Comparison of Random Closed Sets
...........247
7.4.2
Comparison of Point Processes
..............251
7.5
Monotonicity and Comparison of Models of Statistical Physics
253
7.5.1
Monotonicity and Comparison Properties of the
Isiiig
Model
............................253
7.5.2
Comparison of Gibbs Distributions
............259
8
Comparing Risks
...........................265
8.1
Economics of Uncertainty
.....................265
8.1.1
Basics of Stochastic Dominance
..............265
8.1.2
First- and Second-Order Stochastic Dominance
.....266
8.1.3
Stochastic Dominance with
DARA
Utility Functions
. . 209
8.2
Financial Applications
.......................274
8.2.1
Consistency of Mean-deviation Rules
...........274
8.2.2
Portfolio Optimization
...................275
8.3
Ordering of Actuarial Risks
....................278
8.3.1
Bounds for Aggregate Claims of Dependent Risks
. . . . 278
8.3.2
Some Models for Dependent Risks
............289
8.3.3
Indistinguishable Individuals
...............294
8.3.4
Distinguishable Individuals
................296
List of Symbols
..............................299
References
..................................303
Index
.....................................325
Comparison Methods for
Stochastic Models and Risks
Alfred
Müller
University of Karlsruhe, Germany
Dietrich Stoyan
Freiberg University of Mining and Technology, Germany
Stochastic orders are important approximation tools that provide valuable insight
into the behaviour of complex stochastic models. Research into stochastic orders
is blossoming, with many open problems being studied and a wide range of
applications explored. In this book the authors explore the most important
concepts of the field, from the basic univariate theory through to the most current
applications.
*
Comprehensive coverage of the theory and applications of stochastic
orders.
*
Employs a systematic approach with detailed explanation of each concept.
*
Features coverage of univariate and muitivariate stochastic orders.
*
Covers a range of applications, from queueing theory, reliability theory,
statistical physics, actuarial and financial risk, and economics.
»
Written by authors with many years experience in researching stochastic
orders.
Researchers and graduate students studying stochastic orders will find the
comprehensive coverage of the subject ideal for their needs. The range of
applications will benefit those working in applied probability and statistics,
reliability, actuarial science, economics and finance.
|
| any_adam_object | 1 |
| author | Müller, Alfred 1966- Stoyan, Dietrich 1940- |
| author_GND | (DE-588)128790067 (DE-588)115587551 |
| author_facet | Müller, Alfred 1966- Stoyan, Dietrich 1940- |
| author_role | aut aut |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)48754108 (DE-599)BVBBV014080471 |
| dewey-full | 519.2/3 519.2/321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 519.2/3 21 |
| dewey-search | 519.2/3 519.2/3 21 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV014080471 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:17Z |
| institution | BVB |
| isbn | 0471494461 9780471494461 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009644092 |
| oclc_num | 48754108 |
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| physical | XII, 330 S. Ill., graph. Darst. |
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| spelling | Müller, Alfred 1966- Verfasser (DE-588)128790067 aut Comparison methods for stochastic models and risks Alfred Müller ; Dietrich Stoyan Chichester [u.a.] Wiley 2002 XII, 330 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Ordening gtt Stochastische modellen gtt Systèmes stochastiques Stochastic systems Stochastische Ordnung (DE-588)4329325-6 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastische Ordnung (DE-588)4329325-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Stoyan, Dietrich 1940- Verfasser (DE-588)115587551 aut http://www.loc.gov/catdir/description/wiley036/2002284930.html Publisher description http://www.loc.gov/catdir/toc/wiley023/2002284930.html Table of contents Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009644092&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009644092&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Müller, Alfred 1966- Stoyan, Dietrich 1940- Comparison methods for stochastic models and risks Ordening gtt Stochastische modellen gtt Systèmes stochastiques Stochastic systems Stochastische Ordnung (DE-588)4329325-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4329325-6 (DE-588)4057633-4 |
| title | Comparison methods for stochastic models and risks |
| title_auth | Comparison methods for stochastic models and risks |
| title_exact_search | Comparison methods for stochastic models and risks |
| title_full | Comparison methods for stochastic models and risks Alfred Müller ; Dietrich Stoyan |
| title_fullStr | Comparison methods for stochastic models and risks Alfred Müller ; Dietrich Stoyan |
| title_full_unstemmed | Comparison methods for stochastic models and risks Alfred Müller ; Dietrich Stoyan |
| title_short | Comparison methods for stochastic models and risks |
| title_sort | comparison methods for stochastic models and risks |
| topic | Ordening gtt Stochastische modellen gtt Systèmes stochastiques Stochastic systems Stochastische Ordnung (DE-588)4329325-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Ordening Stochastische modellen Systèmes stochastiques Stochastic systems Stochastische Ordnung Stochastisches Modell |
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