Bifurcations of one dimensional stochastic differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Berlin, Humboldt-Univ., Diss., 2001 |
| Physical Description: | V, 194 S. |
| ISBN: | 3897225964 |
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MARC
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| 245 | 1 | 0 | |a Bifurcations of one dimensional stochastic differential equations |c von Marcus Steinkamp |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2000 | |
| 300 | |a V, 194 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Zugl.: Berlin, Humboldt-Univ., Diss., 2001 | ||
| 650 | 7 | |a Bifurcation, Théorie de la |2 ram | |
| 650 | 7 | |a Systèmes dynamiques aléatoires |2 ram | |
| 650 | 7 | |a Équations différentielles stochastiques |2 ram | |
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| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Zufälliges dynamisches System |0 (DE-588)4335207-8 |D s |
| 689 | 0 | 1 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
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| _version_ | 1807229240563728384 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
1
INVARIANT
MEASURES
FOR
RANDOM
DYNAMICAL
SYSTEMS
INDUCED
BY
ONE-DIMENSIONAL
STOCHASTIC
DIFFERENTIAL
EQUATIONS
7
1.1
RANDOM
DYNAMICAL
SYSTEMS
.
7
INVARIANT
MEASURES
.
12
RANDOM
DYNAMICAL
SYSTEMS
ON
THE
REAL
LINE
.
15
1.2
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
20
GENERATION
OF
RDS
FROM
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
21
DIFFUSION
.
23
THE
BACKWARD
EQUATION
.
27
1.3
EXISTENCE
OF
INVARIANT
MEASURES
AND
COMPLETENESS
.
28
1.4
NORMALIZATION
OF
THE
SPEED
MEASURE
.
35
NORMALIZATION
AT
SHUNTS
.
36
NORMALIZATION
AT
FIXED
POINTS
.
37
NORMALIZATION
AT
INFINITY
.
43
2
BIFURCATION
49
2.1
DETERMINISTIC
BIFURCATION
.
49
2.2
CONVERGENCE
OF
RANDOM
MEASURES
.
51
2.3
DEFINITIONS
AND
PREPARATIONS
.
53
2.4
PARAMETER
DEPENDENT
STOCHASTIC
DIFFERENTIAL
EQUATIONS
AND
RANDOM
DYNAMICAL
SYS
TEMS
.
57
2.5
POLE
RATES
FOR
PARAMETER
DEPENDENT
INTEGRALS
.
64
2.6
PHENOMENOLOGICAL
BIFURCATION
.
79
IV
CONTENTS
3
EXAMPLES
AND
FIGURES
83
3.1
LOCAL
(0,0,0,
1)-BIFURCATION
.
85
3.2
FIGURES
.
96
3.3
SENSITIVE
DEPENDENTS
OF
BIFURCATION
SCENARIOS
.
102
4
CLASSIFICATION
OF
BIFURCATIONS
WITH
POLYNOMIAL
DRIFT
AND
MONOMIAL
DIFFUSION
105
4.1
BASIC
SETUP
.
106
4.2
CONVERGENCE
RATE
OF
THE
SPEED
MEASURE
AT
ZERO
.
106
CONVERGENCE
RATE
FOR
NON
LINEAR
DIFFUSION
.
107
CONVERGENCE
RATE
FOR
LINEAR
DIFFUSION
.
119
4.3
CONVERGENCE
RATE
OF
THE
SPEED
MEASURE
AT
INFINITY
.
120
4.4
CLASSIFICATION
.
123
WEAK
CONVERGENCE
.
123
THE
CLASSIFICATION
THEOREM
.
130
CLASSIFICATION
FOR
LINEAR
DIFFUSION
.
134
5
CLASSIFICATION
OF
BIFURCATIONS
FOR
SMOOTH
DRIFT
AND
DIFFUSION
FUNCTIONS
135
5.1
AN
EXAMPLE
.
136
5.2
BASIC
SETUP
.
138
5.3
BEHAVIOUR
AT
INFINITY
.
139
UNIFORMLY
NORMALIZATION
OF
THE
SPEED
MEASURE
AT
INFINITY
.
139
A
FIRST
CLASSIFICATION
.
144
5.4
WEAK
CONVERGENCE
.
147
5.5
CLASSIFICATION
.
160
5.6
EXAMPLES
.
164
6
MOMENTUM
TRADERS
AND
INSTABILITIES
OF
FINANCIAL
MARKETS
165
6.1
INTRODUCTION
.
165
6.2
ZEEMAN
'
S
MODEL
REVISITED
.
166
6.3
THE
STOCHASTIC
MODEL
.
170
6.4
ERGODIC
INVARIANT
MEASURES
AND
WEAK
CONVERGENCE
.
171
BIBLIOGRAPHY
175
CONTENTS
V
LIST
OF
FIGURES
181
LIST
OF
TABLES
185
LIST
OF
ASSUMPTIONS
187
LIST
OF
SYMBOLS
191
INDEX
193 |
| any_adam_object | 1 |
| author | Steinkamp, Marcus 1969- |
| author_GND | (DE-588)12263893X |
| author_facet | Steinkamp, Marcus 1969- |
| author_role | aut |
| author_sort | Steinkamp, Marcus 1969- |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV013585828 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)469325296 (DE-599)BVBBV013585828 |
| dewey-full | 519.2 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics 515 - Analysis |
| dewey-raw | 519.2 515.35 |
| dewey-search | 519.2 515.35 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013585828 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-13T00:15:08Z |
| institution | BVB |
| isbn | 3897225964 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009279162 |
| oclc_num | 469325296 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-29T |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-29T |
| physical | V, 194 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Steinkamp, Marcus 1969- Verfasser (DE-588)12263893X aut Bifurcations of one dimensional stochastic differential equations von Marcus Steinkamp Berlin Logos-Verl. 2000 V, 194 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Berlin, Humboldt-Univ., Diss., 2001 Bifurcation, Théorie de la ram Systèmes dynamiques aléatoires ram Équations différentielles stochastiques ram Dimension 1 (DE-588)4323094-5 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Zufälliges dynamisches System (DE-588)4335207-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zufälliges dynamisches System (DE-588)4335207-8 s Stochastische Differentialgleichung (DE-588)4057621-8 s Dimension 1 (DE-588)4323094-5 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009279162&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steinkamp, Marcus 1969- Bifurcations of one dimensional stochastic differential equations Bifurcation, Théorie de la ram Systèmes dynamiques aléatoires ram Équations différentielles stochastiques ram Dimension 1 (DE-588)4323094-5 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4323094-5 (DE-588)4078889-1 (DE-588)4335207-8 (DE-588)4057621-8 (DE-588)4113937-9 |
| title | Bifurcations of one dimensional stochastic differential equations |
| title_auth | Bifurcations of one dimensional stochastic differential equations |
| title_exact_search | Bifurcations of one dimensional stochastic differential equations |
| title_full | Bifurcations of one dimensional stochastic differential equations von Marcus Steinkamp |
| title_fullStr | Bifurcations of one dimensional stochastic differential equations von Marcus Steinkamp |
| title_full_unstemmed | Bifurcations of one dimensional stochastic differential equations von Marcus Steinkamp |
| title_short | Bifurcations of one dimensional stochastic differential equations |
| title_sort | bifurcations of one dimensional stochastic differential equations |
| topic | Bifurcation, Théorie de la ram Systèmes dynamiques aléatoires ram Équations différentielles stochastiques ram Dimension 1 (DE-588)4323094-5 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Bifurcation, Théorie de la Systèmes dynamiques aléatoires Équations différentielles stochastiques Dimension 1 Verzweigung Mathematik Zufälliges dynamisches System Stochastische Differentialgleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009279162&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT steinkampmarcus bifurcationsofonedimensionalstochasticdifferentialequations |