Stochastic integration and differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2005]
|
| Ausgabe: | Second edition, Version 2.1, corrected 3rd. printing |
| Schriftenreihe: | Stochastic modelling and applied probability
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xiii, 419 Seiten |
| ISBN: | 9783642055607 9783540003137 3540003134 |
Internformat
MARC
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| 100 | 1 | |a Protter, Philip E. |d 1949- |e Verfasser |0 (DE-588)121454304 |4 aut | |
| 245 | 1 | 0 | |a Stochastic integration and differential equations |c Philip E. Protter |
| 250 | |a Second edition, Version 2.1, corrected 3rd. printing | ||
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2005] | |
| 264 | 4 | |c © 2005 | |
| 300 | |a xiii, 419 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Stochastic modelling and applied probability |v 21 | |
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| 689 | 2 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-013345061 | ||
Datensatz im Suchindex
| _version_ | 1804133587261325312 |
|---|---|
| adam_text | Contents
Introduction
................................................... 1
I Preliminaries
..............................................
З
1
Basic Definitions and Notation
............................ 3
2
Martingales
............................................. 7
3
The
Poisson
Process and Brownian Motion
................. 12
4
Levy Processes
.......................................... 20
5
Why the Usual Hypotheses?
.............................. 34
6
Local Martingales
....................................... 37
7
Stieltjes
Integration and Change of Variables
................ 39
8
Naïve
Stochastic Integration is Impossible
.................. 43
Bibliographic Notes
.......................................... 44
Exercises for Chapter I
....................................... 45
II Semimartingales and Stochastic Integrals
.................. 51
1
Introduction to Semimartingales
........................... 51
2
Stability Properties of Semimartingales
..................... 52
3
Elementary Examples of Semimartingales
................... 54
4
Stochastic Integrals
...................................... 56
5
Properties of Stochastic Integrals
.......................... 60
6
The Quadratic Variation of
a Semimartingale
............... 66
7
Itô s
Formula (Change of Variables)
........................ 78
8
Applications of
Itô s
Formula
............................. 84
Bibliographic Notes
.......................................... 92
Exercises for Chapter II
...................................... 94
III Semimartingales and Decomposable Processes
.............101
1
Introduction
............................................101
2
The Classification of Stopping Times
.......................104
3
The Doob-Meyer Decompositions
..........................106
4
Quasimartingales
........................................117
5
Compensators
...........................................119
6
The Fundamental Theorem of Local Martingales
............126
7
Classical Semimartingales
................................129
8
Girsanov s Theorem
.....................................133
9
The Bichteler-Dellacherie Theorem
........................146
Bibliographic Notes
..........................................149
Exercises for Chapter III
......................................150
IV General Stochastic Integration and Local Times
...........155
1
Introduction
............................................155
2
Stochastic Integration for Predictable Integrands
............155
3
Martingale Representation
................................180
4
Martingale Duality and the Jacod-Yor Theorem on
Martingale Representation
................................195
5
Examples of Martingale Representation
....................203
6
Stochastic Integration Depending on a Parameter
............208
7
Local Times
............................................213
8
Azéma s
Martingale
......................................232
9
Sigma Martingales
.......................................237
Bibliographic Notes
..........................................240
Exercises for Chapter IV
......................................241
V Stochastic Differential Equations
..........................249
1
Introduction
............................................249
2
The H_p Norms for Semimartingales
........................250
3
Existence and Uniqueness of Solutions
.....................255
4
Stability of Stochastic Differential Equations
................263
5
Fisk-Stratonovich Integrals and Differential Equations
........277
6
The Markov Nature of Solutions
...........................297
7
Flows of Stochastic Differential Equations: Continuity and
Differentiability
.........................................307
8
Flows as Diffeomorphisms: The Continuous Case
............317
9
General Stochastic Exponentials and Linear Equations
.......328
10
Flows as Diffeomorphisms: The General Case
...............335
11
Eclectic Useful Results on Stochastic Differential Equations
... 345
Bibliographic Notes
..........................................354
Exercises for Chapter V
......................................355
VI Expansion of Filtrations
...................................363
1
Introduction
............................................363
2
Initial Expansions
.......................................364
3
Progressive Expansions
...................................378
4
Time Reversal
..........................................385
Bibliographic Notes
..........................................391
Exercises for Chapter VI
......................................392
References
.....................................................397
Subject Index
.................................................411
|
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| ctrlnum | (OCoLC)635298984 (DE-599)BVBBV020023724 |
| discipline | Mathematik |
| edition | Second edition, Version 2.1, corrected 3rd. printing |
| format | Book |
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| id | DE-604.BV020023724 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:11:05Z |
| institution | BVB |
| isbn | 9783642055607 9783540003137 3540003134 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013345061 |
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| physical | xiii, 419 Seiten |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spelling | Protter, Philip E. 1949- Verfasser (DE-588)121454304 aut Stochastic integration and differential equations Philip E. Protter Second edition, Version 2.1, corrected 3rd. printing Berlin ; Heidelberg Springer [2005] © 2005 xiii, 419 Seiten txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 21 Hier auch später erschienene, unveränderte Nachdrucke Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Martingal (DE-588)4126466-6 s Stochastisches Integral (DE-588)4126478-2 s Erscheint auch als Online-Ausgabe 978-3-662-10061-5 Stochastic modelling and applied probability 21 (DE-604)BV019623501 21 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013345061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Protter, Philip E. 1949- Stochastic integration and differential equations Stochastic modelling and applied probability Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4126478-2 (DE-588)4126466-6 |
| title | Stochastic integration and differential equations |
| title_auth | Stochastic integration and differential equations |
| title_exact_search | Stochastic integration and differential equations |
| title_full | Stochastic integration and differential equations Philip E. Protter |
| title_fullStr | Stochastic integration and differential equations Philip E. Protter |
| title_full_unstemmed | Stochastic integration and differential equations Philip E. Protter |
| title_short | Stochastic integration and differential equations |
| title_sort | stochastic integration and differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Stochastische Differentialgleichung Stochastisches Integral Martingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013345061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
| work_keys_str_mv | AT protterphilipe stochasticintegrationanddifferentialequations |