Stochastic differential equations: an introduction with applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Ausgabe: | 5. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 311 - 316 |
| Beschreibung: | XIX, 324 S. graph. Darst. |
| ISBN: | 3540637206 |
Internformat
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| 100 | 1 | |a Øksendal, Bernt K. |d 1945- |e Verfasser |0 (DE-588)128742054 |4 aut | |
| 245 | 1 | 0 | |a Stochastic differential equations |b an introduction with applications |c Bernt Øksendal |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XIX, 324 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. 311 - 316 | ||
| 650 | 7 | |a Analise de series temporais |2 larpcal | |
| 650 | 7 | |a Analise estocastica |2 larpcal | |
| 650 | 7 | |a Stochastische differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Toepassingen |2 gtt | |
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007941121 | |
Datensatz im Suchindex
| _version_ | 1807501240618188800 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
1.
INTRODUCTION
.
1
1.1
STOCHASTIC
ANALOGS
OF
CLASSICAL
DIFFERENTIAL
EQUATIONS
.
1
1.2
FILTERING
PROBLEMS
.
2
1.3
STOCHASTIC
APPROACH
TO
DETERMINISTIC
BOUNDARY
VALUE
PROBLEMS
.
2
1.4
OPTIMAL
STOPPING
.
3
1.5
STOCHASTIC
CONTROL
.
4
1.6
MATHEMATICAL
FINANCE
.
4
2.
SOME
MATHEMATICAL
PRELIMINARIES
.
7
2.1
PROBABILITY
SPACES,
RANDOM
VARIABLES
AND
STOCHASTIC
PROCESSES
7
2.2
AN
IMPORTANT
EXAMPLE:
BROWNIAN
MOTION
.
11
EXERCISES
.
14
3.
ITO
INTEGRALS
.
21
3.1
CONSTRUCTION
OF
THE
ITO
INTEGRAL
.
21
3.2
SOME
PROPERTIES
OF
THE
ITO
INTEGRAL
.
30
3.3
EXTENSIONS
OF
THE
ITO
INTEGRAL
.
34
EXERCISES
.
37
4.
THE
ITO
FORMULA
AND
THE
MARTINGALE
REPRESENTATION
THEOREM
.
43
4.1
THE
1-DIMENSIONAL
ITO
FORMULA
.
43
4.2
THE
MULTI-DIMENSIONAL
ITO
FORMULA
.
48
4.3
THE
MARTINGALE
REPRESENTATION
THEOREM
.
49
EXERCISES
.
54
5.
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
61
5.1
EXAMPLES
AND
SOME
SOLUTION
METHODS
.
61
5.2
AN
EXISTENCE
AND
UNIQUENESS
RESULT
.
66
5.3
WEAK
AND
STRONG
SOLUTIONS
.
70
EXERCISES
.
72
6.
THE
FILTERING
PROBLEM
.
79
6.1
INTRODUCTION
.
79
6.2
THE
1-DIMENSIONAL
LINEAR
FILTERING
PROBLEM
.
81
6.3
THE
MULTIDIMENSIONAL
LINEAR
FILTERING
PROBLEM
.
100
EXERCISES
.
101
7.
DIFFUSIONS:
BASIC
PROPERTIES
.
107
7.1
THE
MARKOV
PROPERTY
.
107
7.2
THE
STRONG
MARKOV
PROPERTY
.
110
7.3
THE
GENERATOR
OF
AN
ITO
DIFFUSION
.
115
7.4
THE
DYNKIN
FORMULA
.
118
7.5
THE
CHARACTERISTIC
OPERATOR
.
120
EXERCISES
.
122
8.
OTHER
TOPICS
IN
DIFFUSION
THEORY
.
131
8.1
KOLMOGOROV
'
S
BACKWARD
EQUATION.
THE
RESOLVENT
.
131
8.2
THE
FEYNMAN-KAC
FORMULA.
KILLING
.
135
8.3
THE
MARTINGALE
PROBLEM
.
138
8.4
WHEN
IS
AN
ITO
PROCESS
A
DIFFUSION?
.
140
8.5
RANDOM
TIME
CHANGE
.
146
8.6
THE
GIRSANOV
THEOREM
.
152
EXERCISES
.
158
9.
APPLICATIONS
TO
BOUNDARY
VALUE
PROBLEMS
.
167
9.1
THE
COMBINED
DIRICHLET-POISSON
PROBLEM.
UNIQUENESS
.
167
9.2
THE
DIRICHLET
PROBLEM.
REGULAR
POINTS
.
169
9.3
THE
POISSON
PROBLEM
.
181
EXERCISES
.
188
10.
APPLICATION
TO
OPTIMAL
STOPPING
.
195
10.1
THE
TIME-HOMOGENEOUS
CASE
.
195
10.2
THE
TIME-INHOMOGENEOUS
CASE
.
207
10.3
OPTIMAL
STOPPING
PROBLEMS
INVOLVING
AN
INTEGRAL
.
212
10.4
CONNECTION
WITH
VARIATIONAL
INEQUALITIES
.
214
EXERCISES
.
218
11.
APPLICATION
TO
STOCHASTIC
CONTROL
.
225
11.1
STATEMENT
OF
THE
PROBLEM
.
225
11.2
THE
HAMILTON-JACOBI-BELLMAN
EQUATION
.
227
11.3
STOCHASTIC
CONTROL
PROBLEMS
WITH
TERMINAL
CONDITIONS
.
240
EXERCISES
.
242
12.
APPLICATION
TO
MATHEMATICAL
FINANCE
.
249
12.1
MARKET,
PORTFOLIO
AND
ARBITRAGE
.
249
12.2
ATTAINABILITY
AND
COMPLETENESS
.
258
12.3
OPTION
PRICING
.
266
EXERCISES
.
284
APPENDIX
A:
NORMAL
RANDOM
VARIABLES
.
289
APPENDIX
B:
CONDITIONAL
EXPECTATION
.
293
APPENDIX
C:
UNIFORM
INTEGRABILITY
AND
MARTINGALE
CONVERGENCE
.
295
APPENDIX
D:
AN
APPROXIMATION
RESULT
.
299
SOLUTIONS
AND
ADDITIONAL
HINTS
TO
SOME
OF
THE
EXERCISES
.
303
REFERENCES
.
311
LIST
OF
FREQUENTLY
USED
NOTATION
AND
SYMBOLS
.
317
INDEX
.
321 |
| any_adam_object | 1 |
| author | Øksendal, Bernt K. 1945- |
| author_GND | (DE-588)128742054 |
| author_facet | Øksendal, Bernt K. 1945- |
| author_role | aut |
| author_sort | Øksendal, Bernt K. 1945- |
| author_variant | b k ø bk bkø |
| building | Verbundindex |
| bvnumber | BV011767755 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.23.O47 1998 |
| callnumber-search | QA274.23.O47 1998 |
| callnumber-sort | QA 3274.23 O47 41998 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)38474032 (DE-599)BVBBV011767755 |
| dewey-full | 519.221 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 21 519.2 |
| dewey-search | 519.2 21 519.2 |
| dewey-sort | 3519.2 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 5. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-16T00:18:27Z |
| institution | BVB |
| isbn | 3540637206 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007941121 |
| oclc_num | 38474032 |
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| physical | XIX, 324 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Øksendal, Bernt K. 1945- Verfasser (DE-588)128742054 aut Stochastic differential equations an introduction with applications Bernt Øksendal 5. ed. Berlin [u.a.] Springer 1998 XIX, 324 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 311 - 316 Analise de series temporais larpcal Analise estocastica larpcal Stochastische differentiaalvergelijkingen gtt Toepassingen gtt Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007941121&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Øksendal, Bernt K. 1945- Stochastic differential equations an introduction with applications Analise de series temporais larpcal Analise estocastica larpcal Stochastische differentiaalvergelijkingen gtt Toepassingen gtt Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Stochastic differential equations an introduction with applications |
| title_auth | Stochastic differential equations an introduction with applications |
| title_exact_search | Stochastic differential equations an introduction with applications |
| title_full | Stochastic differential equations an introduction with applications Bernt Øksendal |
| title_fullStr | Stochastic differential equations an introduction with applications Bernt Øksendal |
| title_full_unstemmed | Stochastic differential equations an introduction with applications Bernt Øksendal |
| title_short | Stochastic differential equations |
| title_sort | stochastic differential equations an introduction with applications |
| title_sub | an introduction with applications |
| topic | Analise de series temporais larpcal Analise estocastica larpcal Stochastische differentiaalvergelijkingen gtt Toepassingen gtt Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Analise de series temporais Analise estocastica Stochastische differentiaalvergelijkingen Toepassingen Stochastic differential equations Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007941121&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT øksendalberntk stochasticdifferentialequationsanintroductionwithapplications |