Monte-Carlo-Algorithmen:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Springer-Lehrbuch
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 324 S. Ill., graph. Darst. |
| ISBN: | 9783540891406 9783540891413 |
Staff View
MARC
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| 100 | 1 | |a Müller-Gronbach, Thomas |d 1960- |e Verfasser |0 (DE-588)121930459 |4 aut | |
| 245 | 1 | 0 | |a Monte-Carlo-Algorithmen |c Thomas Müller-Gronbach ; Erich Novak ; Klaus Ritter |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a IX, 324 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
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| _version_ | 1824553982353211393 |
| adam_text | Inhaltsverzeichnis
1 Vorbereitungen................................................ 1
1.1 Zufallszahlengeneratoren.................................... 2
1.2 Wahrscheinlichkeitstheoretische Grundbegriffe.................. 4
1.3 Zufallszahlen und gleichverteilte Zufallsvariablen............... 8
Aufgaben...................................................... 10
2 Algorithmen, Fehler und Kosten................................. 13
2.1 Was ist ein Algorithmus?.................................... 14
2.2 Fehler und Kosten einer Monte Carlo-Methode.................. 16
2.3 Ein Zählproblem........................................... 20
Aufgaben...................................................... 24
3 Das Verfahren der direkten Simulation........................... 27
3.1 Direkte Simulation ......................................... 28
3.2 Erste Beispiele............................................. 30
3.2.1 Die Berechnung von
π
................................ 31
3.2.2 Numerische Integration............................... 32
3.2.3 Eigenschaften von zufälligen Polyedern................. 35
3.2.4 Chancen bei Patience-Spielen.......................... 37
3.2.5 Die Bewertung von Finanzderivaten .................... 38
3.2.6 Ein Ruinproblem .................................... 42
3.3 Grenzwertsätze der Stochastik................................ 42
3.3.1 Das starke Gesetz der großen Zahlen.................... 43
3.3.2 Der zentrale Grenzwertsatz............................ 48
3.4 Die Hoeffding-Ungleichung.................................. 53
3.5 Varianzschätzung und Konfidenzintervalle...................... 56
3.6 Stoppzeiten und Unabhängigkeit.............................. 63
Aufgaben...................................................... 70
Simulation von Verteilungen .................................... 75
4.1 Die Inversionsmethode...................................... 76
4.2 Durchgang von Neutronen durch Materie....................... 79
4.3 Die Verwerfungsmethode.................................... 87
4.4 Simulation von Normalverteilungen........................... 92
4.5 Simulation stochastischer Prozesse............................ 96
4.5.1 Zeit-diskrete Markov-Prozesse......................... 97
4.5.2 Die Brownsche Bewegung und der Poisson-Prozeß........101
4.5.3 Bewertung von Optionen im Black-Scholes-Modell.......110
4.5.4 Ruinwahrscheinlichkeiten im
Cramér-Lundberg-Modell
.... 114
4.5.5 Der sphärische Prozeß und das Dirichlet-Problem.........116
Aufgaben......................................................127
Varianzreduktion..............................................133
5.1
Antithetic Sampling ........................................
134
5.2
Control
Variâtes
............................................139
5.3
Stratified Sampling
.........................................146
5.4
Importance Sampling
.......................................155
5.5 Varianzreduktion zur Verbesserung der Konvergenzordnung.......166
Aufgaben......................................................173
Die
Markov
Chain Monte Carlo-Methode.........................179
6.1 Die Grenzen der direkten Simulation..........................180
6.2 Endliche Markov-Ketten ....................................188
6.2.1 Grundbegriffe.......................................188
6.2.2 Grenzwertsätze........,..............................202
6.3
Markov
Chain Monte Carlo-Algorithmen ......................207
6.4 Ausblick..................................................216
6.4.1 Schnelle Mischung...................................216
6.4.2 Fehlerschranken und Aufwärmzeit......................219
6.4.3 Schnelle Mischung beim Ising-Modell ..................222
6.4.4 Perfekte Simulation..................................226
6.4.5 Markov-Ketten auf konvexen Körpern...................236
Aufgaben......................................................239
Numerische Integration.........................................245
7.1 Deterministische Algorithmen................................247
7.1.1 Grundbegriffe.......................................247
7.1.2 Untere Schranken für minimale Fehler..................254
7.1.3 Multivariate polynomiale Interpolation..................260
7.1.4 Asymptotisch optimale Algorithmen für Fj ..............267
7.1.5 Optimalität von Quadraturformeln......................270
7.2 Randomisierte Algorithmen..................................273
7.2.1 Grundbegriffe.......................................274
7.2.2 Untere Schranken für minimale Fehler ..................278
7.2.3 Asymptotisch optimale Algorithmen für
F¿¡
..............285
7.3 Unendlich-dimensionale Integration...........................287
7.4 Ausblick..................................................297
7.4.1 Funktionen mit beschränkten gemischten Ableitungen.....298
7.4.2 Tractability und der Fluch der Dimension................299
7.4.3 Zur Überlegenheit randomisierter Algorithmen...........302
7.4.4
Average Case-Analyse................................
303
7.4.5
Stochastische
Multilevel-
Verfahren.....................304
Aufgaben......................................................307
Literaturverzeichnis................................................311
Symbolverzeichnis..................................................319
Sachverzeichnis....................................................321
|
| any_adam_object | 1 |
| author | Müller-Gronbach, Thomas 1960- Novak, Erich 1953- Ritter, Klaus 1961- |
| author_GND | (DE-588)121930459 (DE-588)141295422 (DE-588)1143568494 |
| author_facet | Müller-Gronbach, Thomas 1960- Novak, Erich 1953- Ritter, Klaus 1961- |
| author_role | aut aut aut |
| author_sort | Müller-Gronbach, Thomas 1960- |
| author_variant | t m g tmg e n en k r kr |
| building | Verbundindex |
| bvnumber | BV037206390 |
| classification_rvk | QH 239 SK 800 SK 820 SK 840 |
| ctrlnum | (OCoLC)779624537 (DE-599)DNB100003271X |
| dewey-full | 518.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.282 |
| dewey-search | 518.282 |
| dewey-sort | 3518.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften Medizin |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-02-20T06:44:31Z |
| institution | BVB |
| isbn | 9783540891406 9783540891413 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021120527 |
| oclc_num | 779624537 |
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| physical | IX, 324 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer-Lehrbuch |
| spellingShingle | Müller-Gronbach, Thomas 1960- Novak, Erich 1953- Ritter, Klaus 1961- Monte-Carlo-Algorithmen Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4240945-7 |
| title | Monte-Carlo-Algorithmen |
| title_auth | Monte-Carlo-Algorithmen |
| title_exact_search | Monte-Carlo-Algorithmen |
| title_full | Monte-Carlo-Algorithmen Thomas Müller-Gronbach ; Erich Novak ; Klaus Ritter |
| title_fullStr | Monte-Carlo-Algorithmen Thomas Müller-Gronbach ; Erich Novak ; Klaus Ritter |
| title_full_unstemmed | Monte-Carlo-Algorithmen Thomas Müller-Gronbach ; Erich Novak ; Klaus Ritter |
| title_short | Monte-Carlo-Algorithmen |
| title_sort | monte carlo algorithmen |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021120527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mullergronbachthomas montecarloalgorithmen AT novakerich montecarloalgorithmen AT ritterklaus montecarloalgorithmen |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 840 M947 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |