Vector integration and stochastic integration in Banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Series: | Pure and applied mathematics
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 424 S. |
| ISBN: | 0471377384 |
Staff View
MARC
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| 245 | 1 | 0 | |a Vector integration and stochastic integration in Banach spaces |c Nicolae Dinculeanu |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 2000 | |
| 300 | |a XV, 424 S. | ||
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| 490 | 0 | |a Pure and applied mathematics | |
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Record in the Search Index
| _version_ | 1804127898880180224 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1 Vector Integration 1
§./. Preliminaries l
A. Banach spaces l
B. Classes of sets 2
C. Measurable functions 3
D. Simple measurability of operator valued
functions 7
E. Weak measurability 8
F. Integral of step functions 9
G. Totally measurable functions and the
immediate integral 10
H. The Riesz representation theorem 11
I. The classical integral 13
J. The Bochner integral 15
K. Convergence theorems 17
§2. Measures with finite variation 20
A. The variation of vector measures 20
IX
x CONTENTS
B. Boundedness of a additive measures 23
C. Variation of real valued measures 24
D. Integration with respect to vector measures
with finite variation 26
E. The indefinite integral 28
F. Integration with respect to gm 32
G. The Radon Nikodym theorem 36
H. Conditional expectations 43
§5. a additive measures 49
A. a additive measures on a rings 49
B. Uniform a additivity 50
C. Uniform absolute continuity and uniform
a additivity 52
D. Weak a additivity 57
E. Uniform a additivity of indefinite integrals 57
F. Weakly compact sets in LF(n) 60
§4 Measures with finite semivariation 63
A. The semivariation 63
B. Semivariation and norming spaces 66
C. The semivariation of a additive measures 69
D. The family mF%z of measures 71
§5. Integration with respect to a measure with finite
semivariation 77
A. Measurability with respect to a vector
measure 77
B. The seminorm rhFiG(f) 79
C. The space of integrable functions 82
D. The integral 85
E. Convergence theorems 87
F. Properties of the space TD(B,rhF,G) 90
G. Relationship between the spaces TD{m) 92
H. The indefinite integral of measures with
finite semivariation 95
§6. Strong additivity 102
§7. Extension of measures 109
$8. Applications 117
A. The Riesz representation theorem 117
B. Integral representation of continuous
linear operations on V spaces 117
CONTENTS xi
C. Random Gaussian measures 120
Chapter 2 The Stochastic Integral 123
§9. Summable processes 124
A. Notations 124
B. The measure Ix 125
C. Summable processes 126
D. Computation of Ix for predictable
rectangles 127
E. Computation of Ix for stochastic intervals 129
§10. The stochastic integral 133
A. The space TD(JFLv) 133
B. The integral J Hdlx 134
C. A convergence theorem 134
D. The stochastic integral H ¦ X 136
§11. The stochastic integral and stopping times 140
A. Stochastic integral of elementary processes 140
B. Stopping the stochastic integral 146
C. Summabilty of stopped processes 148
D. The jumps of the stochastic integral 151
§12. Convergence theorems 153
A. The completeness of the space LFG{X) 153
B. The Uniform Convergence Theorem 156
C. The Vitali and the Lebesgue Convergence
Theorems 156
D. The stochastic integral of a elementary
and of caglad processes as a pathwise
Stieltjes integral 157
§13. Summability of the stochastic integral 161
§14 Summability criterion 164
A. Quasimartingales and the Doleans
measure 164
B. The summability criterion 168
§15. Local summability and local integrability 171
A. Definitions 171
B. Basic properties 172
C. Convergence theorems 175
xii CONTENTS
D. Additional properties 119
Chapter 3 Martingales 181
§16. Stochastic integral of martingales 181
§17. Square integrable martingales 185
A. Extension of the measure Im 185
B. Summability of square integrable
martingales 188
C. Properties of the space Tf,g(M) 190
D. Isometrical isomorphism of LlFG{M) and
LF{^M)) 193
Chapter 4 Processes with Finite Variation 199
§18. Functions with finite variation and their Stieltjes
integral 200
A. Functions with finite variation 200
B. The variation function g 201
C. The measure associated to a function 203
D. The Stieltjes integral 208
§19. Processes with finite variation 211
A. Definition and properties 211
B. Optional and predictable measures 216
C. The measure nx 217
D. Summability of processes with integrable
variation 233
E. The stochastic integral as a Stieltjes
integral 236
F. The pathwise stochastic integral 239
G. Semilocally summable processes 242
Chapter 5 Processes with Finite Semivariation 243
§20. Functions with finite semivariation and their
Stieltjes integral 244
A. Functions with finite semivariation 244
CONTENTS xiii
B. Semivariation and norming spaces 245
C. The measure associated to a function 247
D. The Stieltjes integral with respect to a
function with finite semivariation 250
§21. Processes with finite semivariation 253
A. The semivariation process 253
B. The measure nx 258
C. Summability of processes with integrable
semivariation 262
D. The pathwise stochastic integral 261
§22. Dual projections 272
A. Dual projection of measures 272
B. Dual projections of processes 274
C. Existence of dual projections 278
D. Processes with locally integrable variation
or semivariation 279
E. Examples of processes with locally
integrable variation or semivariation 281
F. Decomposition of local martingales 285
Chapter 6 The ltd Formula 289
§23. The ltd formula 289
A. Preliminary results 289
B. The vector quadratic variation 296
C. The quadratic variation 298
D. The process of jumps 304
E. ltd s formula 312
Chapter 7 Stochastic Integration in the Plane 321
§24. Preliminaries 321
A. Order relation in R2 321
B. The increment Azz, g 322
C. Right continuity 322
D. The filtration 323
E. The predictable a algebra 323
F. Stopping times 323
xiv CONTENTS
G. Stochastic processes 324
H. Extension of processes from R^_ x £1 to M2 x fi 325
§25. Summable processes 321
A. The measure Ix 321
B. Summable processes 321
C. The seminorm Ix and the space Tf,g{X) 328
D. The integral f Hdlx 328
E. The stochastic integral H ¦ X 329
§26. Properties of the stochastic integral 331
A. Convergence theorems 331
B. Extension of Ix to 7 (oo) 332
C. Existence of left limits of X in LPE 332
D. Some properties of the integral f Hdlx 333
E. Summability of stopped processes 338
F. Summability of the stochastic integral 340
Chapter 8 Two Parameter Martingales 343
§21. Martingales 343
§28. Square integrable martingales 349
A. A decomposition theorem 349
B. The measures IM{ ) 2L2 and /z M) 349
C. Summability of the square integrable
martingales in Hilbert spaces 353
D. The space TF^G{IM) 355
E. Isometric isomorphism of LFG(M) and
L2F^(M)) 557
Chapter 9 Two Parameter Processes with
Finite Variation 363
§29. Functions with finite variation in the plane 363
A. Monotone functions 363
B. Partitions 364
C. Variation corresponding to a partition 366
D. Variation of a function on a rectangle 366
E. Limits of the variation 369
CONTENTS xv
F. The variation function g 374
G. Functions with finite variation 375
H. Functions vanishing outside a quadrant 376
I. Variation of real valued functions 378
J. Lateral limits 379
K. Measures associated to functions 385
L. a additivity of the measure mg 387
M. The Stieltjes integral 390
$30. Processes with finite variation 391
A. Processes with integrable variation 391
B. The measure ^x 391
C. Summability of processes with integrable
variation 400
D. The stochastic integral as a Stieltjes
integral 400
Chapter 10 Two Parameter Processes with
Finite Semivariation 403
31. Functions with finite semivariation in the plane 403
A. Functions with finite semivariation 403
B. Semivariation and norming spaces 405
C. The measure associated to a function 406
D. The Stieltjes integral for functions with
finite semivariation in R2 408
§32. Processes with finite semivariation in the plane 410
A. Processes with finite semivariation 410
B. The measure nx 411
C. Summability of processes with integrable
semivariation 412
References 413
|
| any_adam_object | 1 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013199037 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:40:40Z |
| institution | BVB |
| isbn | 0471377384 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008992332 |
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| physical | XV, 424 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics A Wiley-Interscience publication |
| spelling | Dinculeanu, Nicolae 1925- Verfasser (DE-588)128080493 aut Vector integration and stochastic integration in Banach spaces Nicolae Dinculeanu New York [u.a.] Wiley 2000 XV, 424 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics A Wiley-Interscience publication Vektor - Integration <Mathematik> - Stochastisches Integral - Banach-Raum Banach-Raum (DE-588)4004402-6 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Vektorraum (DE-588)4130622-3 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s Banach-Raum (DE-588)4004402-6 s Vektorraum (DE-588)4130622-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008992332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dinculeanu, Nicolae 1925- Vector integration and stochastic integration in Banach spaces Vektor - Integration <Mathematik> - Stochastisches Integral - Banach-Raum Banach-Raum (DE-588)4004402-6 gnd Stochastisches Integral (DE-588)4126478-2 gnd Vektorraum (DE-588)4130622-3 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4126478-2 (DE-588)4130622-3 |
| title | Vector integration and stochastic integration in Banach spaces |
| title_auth | Vector integration and stochastic integration in Banach spaces |
| title_exact_search | Vector integration and stochastic integration in Banach spaces |
| title_full | Vector integration and stochastic integration in Banach spaces Nicolae Dinculeanu |
| title_fullStr | Vector integration and stochastic integration in Banach spaces Nicolae Dinculeanu |
| title_full_unstemmed | Vector integration and stochastic integration in Banach spaces Nicolae Dinculeanu |
| title_short | Vector integration and stochastic integration in Banach spaces |
| title_sort | vector integration and stochastic integration in banach spaces |
| topic | Vektor - Integration <Mathematik> - Stochastisches Integral - Banach-Raum Banach-Raum (DE-588)4004402-6 gnd Stochastisches Integral (DE-588)4126478-2 gnd Vektorraum (DE-588)4130622-3 gnd |
| topic_facet | Vektor - Integration <Mathematik> - Stochastisches Integral - Banach-Raum Banach-Raum Stochastisches Integral Vektorraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008992332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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