Continuous martingales and Brownian motion:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1994
|
| Edition: | 2. ed. |
| Series: | Grundlehren der mathematischen Wissenschaften
293 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 560 S. |
| ISBN: | 3540576223 0387576223 |
Staff View
MARC
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| 245 | 1 | 0 | |a Continuous martingales and Brownian motion |c Daniel Revuz ; Marc Yor |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a XI, 560 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Martingales (Mathématiques) | |
| 650 | 7 | |a Martingales (Mathématiques) |2 ram | |
| 650 | 4 | |a Mouvement brownien, Processus de | |
| 650 | 7 | |a Mouvement brownien, processus de |2 ram | |
| 650 | 4 | |a Brownian motion processes | |
| 650 | 4 | |a Martingales (Mathematics) | |
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Record in the Search Index
| _version_ | 1807865797309104128 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
CHAPTER
0.
PRELIMINARIES
.
1
§1.
BASIC
NOTATION
.
1
§
2.
MONOTONE
CLASS
THEOREM
.
2
§
3.
COMPLETION
.
3
§4.
FUNCTIONS
OF
FINITE
VARIATION
AND
STIELTJES
INTEGRALS
.
4
§
5.
WEAK
CONVERGENCE
IN
METRIC
SPACES
.
9
§6.
GAUSSIAN
AND
OTHER
RANDOM
VARIABLES
.
12
CHAPTER
I.
INTRODUCTION
.
14
§
1.
EXAMPLES
OF
STOCHASTIC
PROCESSES.
BROWNIAN
MOTION
.
14
§
2.
LOCAL
PROPERTIES
OF
BROWNIAN
PATHS
.
24
§
3.
CANONICAL
PROCESSES
AND
GAUSSIAN
PROCESSES
.
31
§4.
FILTRATIONS
AND
STOPPING
TIMES
.
39
NOTES
AND
COMMENTS
.
46
CHAPTER
II.
MARTINGALES
.
48
§
1.
DEFINITIONS,
MAXIMAL
INEQUALITIES
AND
APPLICATIONS
.
48
§2.
CONVERGENCE
AND
REGULARIZATION
THEOREMS
.
57
§
3.
OPTIONAL
STOPPING
THEOREM
.
64
NOTES
AND
COMMENTS
.
73
CHAPTER
III.
MARKOV
PROCESSES
.
74
§
1.
BASIC
DEFINITIONS
.
74
§
2.
FELLER
PROCESSES
.
83
§
3.
STRONG
MARKOV
PROPERTY
.
97
§4.
SUMMARY
OF
RESULTS
ON
LEVY
PROCESSES
.
109
NOTES
AND
COMMENTS
.
112
CHAPTER
IV.
STOCHASTIC
INTEGRATION
.
113
§1.
QUADRATIC
VARIATIONS
.
113
§
2.
STOCHASTIC
INTEGRALS
.
129
§3.
IT6
'
S
FORMULA
AND
FIRST
APPLICATIONS
.
138
§4.
BURKHOLDER-DAVIS-GUNDY
INEQUALITIES
.
138
X
TABLE
OF
CONTENTS
§
5.
PREDICTABLE
PROCESSES
.
163
NOTES
AND
COMMENTS
.
168
CHAPTER
V.
REPRESENTATION
OF
MARTINGALES
.
171
§
1.
CONTINUOUS
MARTINGALES
AS
TIME-CHANGED
BROWNIAN
MOTIONS
.
171
§2.
CONFORMAL
MARTINGALES
AND
PLANAR
BROWNIAN
MOTION
.
181
§
3.
BROWNIAN
MARTINGALES
.
190
§4.
INTEGRAL
REPRESENTATIONS
.
200
NOTES
AND
COMMENTS
.
207
CHAPTER
VI.
LOCAL
TIMES
.
212
§
1.
DEFINITION
AND
FIRST
PROPERTIES
.
212
§
2.
THE
LOCAL
TIME
OF
BROWNIAN
MOTION
.
229
§
3.
THE
THREE-DIMENSIONAL
BESSEL
PROCESS
.
240
§
4.
FIRST
ORDER
CALCULUS
.
249
§
5.
THE
SKOROKHOD
STOPPING
PROBLEM
.
258
NOTES
AND
COMMENTS
.
264
CHAPTER
VII.
GENERATORS
AND
TIME
REVERSAL
.
268
§1.
INFINITESIMAL
GENERATORS
.
268
§2.
DIFFUSIONS
AND
ITD
PROCESSES
.
280
§
3.
LINEAR
CONTINUOUS
MARKOV
PROCESSES
.
287
§4.
TIME
REVERSAL
AND
APPLICATIONS
.
299
NOTES
AND
COMMENTS
.
309
CHAPTER
VIII.
GIRSANOV
'
S
THEOREM
AND
FIRST
APPLICATIONS
.
311
§1.
GIRSANOV
'
S
THEOREM
.
311
§
2.
APPLICATION
OF
GIRSANOV
'
S
THEOREM
TO
THE
STUDY
OF
WIENER
'
S
SPACE
.
324
§
3.
FUNCTIONALS
AND
TRANSFORMATIONS
OF
DIFFUSION
PROCESSES
.
335.
NOTES
AND
COMMENTS
.
346
CHAPTER
IX.
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
349
§
1.
FORMAL
DEFINITIONS
AND
UNIQUENESS
.
349
§
2.
EXISTENCE
AND
UNIQUENESS
IN
THE
CASE
OF
LIPSCHITZ
COEFFICIENTS
.
359
§
3.
THE
CASE
OF
HOLDER
COEFFICIENTS
IN
DIMENSION
ONE
.
369
NOTES
AND
COMMENTS
.
380
CHAPTER
X.
ADDITIVE
FUNCTIONALS
OF
BROWNIAN
MOTION
.
382
§
1.
GENERAL
DEFINITIONS
.
382
§2.
REPRESENTATION
THEOREM
FOR
ADDITIVE
FUNCTIONALS
OF
LINEAR
BROWNIAN
MOTION
.
390
§
3.
ERGODIC THEOREMS
FOR
ADDITIVE
FUNCTIONALS
.
404
§
4.
ASYMPTOTIC
RESULTS
FOR
THE
PLANAR
BROWNIAN
MOTION
.
411
NOTES
AND
COMMENTS
.
417
TABLE
OF
CONTENTS
XI
CHAPTER
XI.
BESSEL
PROCESSES
AND
RAY-KNIGHT
THEOREMS
.
420
§
1.
BESSEL
PROCESSES
.
420
§
2.
RAY-KNIGHT
THEOREMS
.
433
§
3.
BESSEL
BRIDGES
.
441
NOTES
AND
COMMENTS
.
446
CHAPTER
XII.
EXCURSIONS
.
448
§
1.
PREREQUISITES
ON
POISSON
POINT
PROCESSES
.
448
§
2.
THE
EXCURSION
PROCESS
OF
BROWNIAN
MOTION
.
456
§
3.
EXCURSIONS
STRADDLING
A
GIVEN
TIME
.
463
§4.
DESCRIPTIONS
OF
IT6
'
S
MEASURE
AND
APPLICATIONS
.
469
NOTES
AND
COMMENTS
.
485
CHAPTER
XIII.
LIMIT
THEOREMS
IN
DISTRIBUTION
.
487
§
1.
CONVERGENCE
IN
DISTRIBUTION
.
487
§
2.
ASYMPTOTIC
BEHAVIOR
OF
ADDITIVE
FUNCTIONALS
OF
BROWNIAN
MOTION
494
§
3.
ASYMPTOTIC
PROPERTIES
OF
PLANAR
BROWNIAN
MOTION
.
503
NOTES
AND
COMMENTS
.
513
APPENDIX
.
515
§
1.
GRONWALL
'
S
LEMMA
.
515
§
2.
DISTRIBUTIONS
.
516
§
3.
CONVEX
FUNCTIONS
.
519
§4.
HAUSDORFF
MEASURES
AND
DIMENSION
.
520
§
5.
ERGODIC
THEORY
.
520
§6.
PROBABILITIES
ON
FUNCTION
SPACES
520
BIBLIOGRAPHY
.
523
INDEX
OF
NOTATION
.
549
INDEX
OF
TERMS
.
553
CATALOGUE
.
559 |
| any_adam_object | 1 |
| author | Revuz, Daniel 1936- Yor, Marc 1949-2014 |
| author_GND | (DE-588)120628619 (DE-588)120628635 |
| author_facet | Revuz, Daniel 1936- Yor, Marc 1949-2014 |
| author_role | aut aut |
| author_sort | Revuz, Daniel 1936- |
| author_variant | d r dr m y my |
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| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)30319511 (DE-599)BVBBV009671414 |
| dewey-full | 519.2/87 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/87 |
| dewey-search | 519.2/87 |
| dewey-sort | 3519.2 287 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009671414 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:52:57Z |
| institution | BVB |
| isbn | 3540576223 0387576223 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006396560 |
| oclc_num | 30319511 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-824 DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-824 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 560 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Revuz, Daniel 1936- Verfasser (DE-588)120628619 aut Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor 2. ed. Berlin u.a. Springer 1994 XI, 560 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 293 Brownse beweging gtt Martingalen gtt Martingales (Mathématiques) Martingales (Mathématiques) ram Mouvement brownien, Processus de Mouvement brownien, processus de ram Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Martingal (DE-588)4126466-6 s DE-604 Stochastische Analysis (DE-588)4132272-1 s Martingaltheorie (DE-588)4168982-3 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Yor, Marc 1949-2014 Verfasser (DE-588)120628635 aut Grundlehren der mathematischen Wissenschaften 293 (DE-604)BV000000395 293 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396560&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Revuz, Daniel 1936- Yor, Marc 1949-2014 Continuous martingales and Brownian motion Grundlehren der mathematischen Wissenschaften Brownse beweging gtt Martingalen gtt Martingales (Mathématiques) Martingales (Mathématiques) ram Mouvement brownien, Processus de Mouvement brownien, processus de ram Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd Martingaltheorie (DE-588)4168982-3 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4168982-3 (DE-588)4128328-4 (DE-588)4126466-6 (DE-588)4057630-9 |
| title | Continuous martingales and Brownian motion |
| title_auth | Continuous martingales and Brownian motion |
| title_exact_search | Continuous martingales and Brownian motion |
| title_full | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_fullStr | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_full_unstemmed | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_short | Continuous martingales and Brownian motion |
| title_sort | continuous martingales and brownian motion |
| topic | Brownse beweging gtt Martingalen gtt Martingales (Mathématiques) Martingales (Mathématiques) ram Mouvement brownien, Processus de Mouvement brownien, processus de ram Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd Martingaltheorie (DE-588)4168982-3 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Brownse beweging Martingalen Martingales (Mathématiques) Mouvement brownien, Processus de Mouvement brownien, processus de Brownian motion processes Martingales (Mathematics) Stochastische Analysis Martingaltheorie Brownsche Bewegung Martingal Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396560&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT revuzdaniel continuousmartingalesandbrownianmotion AT yormarc continuousmartingalesandbrownianmotion |