Introduction to stochastic integration
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
1990
|
| Ausgabe: | second edition |
| Schriftenreihe: | Probability and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV004197089 | ||
| 003 | DE-604 | ||
| 005 | 20231107 | ||
| 007 | t| | ||
| 008 | 910110s1990 xx |||| |||| 00||| eng d | ||
| 020 | |a 0817633863 |9 0-8176-3386-3 | ||
| 020 | |a 3764333863 |9 3-7643-3386-3 | ||
| 035 | |a (OCoLC)21949793 | ||
| 035 | |a (DE-599)BVBBV004197089 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-91G |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-384 |a DE-83 |a DE-11 |a DE-188 |a DE-521 | ||
| 050 | 0 | |a QA274.22 | |
| 082 | 0 | |a 519.2 |2 20 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60H05 |2 msc/1990 | ||
| 084 | |a MAT 606f |2 stub | ||
| 084 | |a MAT 285f |2 stub | ||
| 100 | 1 | |a Chung, Kai Lai |d 1917-2009 |0 (DE-588)136125484 |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic integration |c K. L. Chung ; R. J. Williams |
| 250 | |a second edition | ||
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1990 | |
| 300 | |a xv, 276 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Probability and its applications | |
| 650 | 4 | |a Intégrales stochastiques | |
| 650 | 7 | |a Intégrales stochastiques |2 ram | |
| 650 | 4 | |a Martingales (Mathématiques) | |
| 650 | 7 | |a Martingales (Mathématiques) |2 ram | |
| 650 | 7 | |a Stochastische integratie |2 gtt | |
| 650 | 4 | |a Martingales (Mathematics) | |
| 650 | 4 | |a Stochastic integrals | |
| 650 | 0 | 7 | |a Stochastisches Integral |0 (DE-588)4126478-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Martingal |0 (DE-588)4126466-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Stochastisches Integral |0 (DE-588)4126478-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Martingal |0 (DE-588)4126466-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Williams, Ruth J. |d 1955- |0 (DE-588)172452910 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4612-4480-6 |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002614534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-002614534 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 605f 2001 A 10617 0102 MAT 605f 2001 A 10618 0202 MAT 605f 2002 A 1243(2) |
|---|---|
| DE-BY-TUM_katkey | 511082 |
| DE-BY-TUM_location | 01 02 |
| DE-BY-TUM_media_number | 040020170094 040020054526 040020670680 |
| _version_ | 1820882671142699008 |
| adam_text | TABLE OF CONTENTS
PREFACE v
PREFACE TO THE FIRST EDITION vii
ABBREVIATIONS AND SYMBOLS xiii
1. PRELIMINARIES 1
1.1 Notations and Conventions 1
1.2 Measurability, Lp Spaces and Monotone Class Theorems 2
1.3 Functions of Bounded Variation and Stieltjes Integrals 4
1.4 Probability Space, Random Variables, Filtration 6
1.5 Convergence, Conditioning 7
1.6 Stochastic Processes 8
1.7 Optional Times 9
1.8 Two Canonical Processes 10
1.9 Martingales 13
1.10 Local Martingales 18
1.11 Exercises 21
x TABLE OF CONTENTS
2. DEFINITION OF THE STOCHASTIC INTEGRAL 23
2.1 Introduction 23
2.2 Predictable Sets and Processes 25
2.3 Stochastic Intervals 26
2.4 Measure on the Predictable Sets 32
2.5 Definition of the Stochastic Integral 34
2.6 Extension to Local Integrators and Integrands 43
2.7 Substitution Formula 48
2.8 A Sufficient Condition for Extendability of z 50
2.9 Exercises 54
3. EXTENSION OF THE PREDICTABLE INTEGRANDS 57
3.1 Introduction 57
3.2 Relationship between V, O, and Adapted Processes 57
3.3 Extension of the Integrands 63
3.4 A Historical Note 71
3.5 Exercises 73
4. QUADRATIC VARIATION PROCESS 75
4.1 Introduction 75
4.2 Definition and Characterization of Quadratic Variation 75
4.3 Properties of Quadratic Variation for an £2 martingale 79
4.4 Direct Definition of hm 82
4.5 Decomposition of (M)2 86
4.6 A Limit Theorem 89
4.7 Exercises 90
5. THE ITO FORMULA 93
5.1 Introduction 93
5.2 One dimensional Ito Formula 94
5.3 Mutual Variation Process 99
5.4 Multi dimensional Ito Formula 109
5.5 Exercises 112
TABLE OF CONTENTS xi
6. APPLICATIONS OF THE ITO FORMULA 117
6.1 Characterization of Brownian Motion 117
6.2 Exponential Processes 120
6.3 A Family of Martingales Generated by M 123
6.4 Feynman Kac Functional and the Schrodinger Equation 128
6.5 Exercises 136
7. LOCAL TIME AND TANAKA S FORMULA 141
7.1 Introduction 141
7.2 Local Time 142
7.3 Tanaka s Formula 150
7.4 Proof of Lemma 7.2 153
7.5 Exercises 155
8. REFLECTED BROWNIAN MOTIONS 157
8.1 Introduction 157
8.2 Brownian Motion Reflected at Zero 158
8.3 Analytical Theory of Z via the Ito Formula 161
8.4 Approximations in Storage Theory 163
8.5 Reflected Brownian Motions in a Wedge 174
8.6 Alternative Derivation of Equation (8.7) 178
8.7 Exercises 181
9. GENERALIZED ITO FORMULA,
CHANGE OF TIME AND MEASURE 183
9.1 Introduction 183
9.2 Generalized Ito Formula 184
9.3 Change of Time 187
9.4 Change of Measure 197
9.5 Exercises 214
xii TABLE OF CONTENTS
10. STOCHASTIC DIFFERENTIAL EQUATIONS 217
10.1 Introduction 217
10.2 Existence and Uniqueness for Lipschitz Coefficients 220
10.3 Strong Markov Property of the Solution 235
10.4 Strong and Weak Solutions 243
10.5 Examples 252
10.6 Exercises 262
REFERENCES 265
INDEX 273
|
| any_adam_object | 1 |
| author | Chung, Kai Lai 1917-2009 Williams, Ruth J. 1955- |
| author_GND | (DE-588)136125484 (DE-588)172452910 |
| author_facet | Chung, Kai Lai 1917-2009 Williams, Ruth J. 1955- |
| author_role | aut aut |
| author_sort | Chung, Kai Lai 1917-2009 |
| author_variant | k l c kl klc r j w rj rjw |
| building | Verbundindex |
| bvnumber | BV004197089 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.22 |
| callnumber-search | QA274.22 |
| callnumber-sort | QA 3274.22 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f MAT 285f |
| ctrlnum | (OCoLC)21949793 (DE-599)BVBBV004197089 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 |
| edition | second edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02270nam a2200577 c 4500</leader><controlfield tag="001">BV004197089</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20231107 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">910110s1990 xx |||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817633863</subfield><subfield code="9">0-8176-3386-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764333863</subfield><subfield code="9">3-7643-3386-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)21949793</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004197089</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-521</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H05</subfield><subfield code="2">msc/1990</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 606f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 285f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chung, Kai Lai</subfield><subfield code="d">1917-2009</subfield><subfield code="0">(DE-588)136125484</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to stochastic integration</subfield><subfield code="c">K. L. Chung ; R. J. Williams</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston ; Basel ; Berlin</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xv, 276 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Probability and its applications</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intégrales stochastiques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Intégrales stochastiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Martingales (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Martingales (Mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastische integratie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Martingales (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic integrals</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Martingal</subfield><subfield code="0">(DE-588)4126466-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Martingal</subfield><subfield code="0">(DE-588)4126466-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Williams, Ruth J.</subfield><subfield code="d">1955-</subfield><subfield code="0">(DE-588)172452910</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4612-4480-6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002614534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002614534</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV004197089 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T11:09:57Z |
| institution | BVB |
| isbn | 0817633863 3764333863 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002614534 |
| oclc_num | 21949793 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-384 DE-83 DE-11 DE-188 DE-521 |
| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-384 DE-83 DE-11 DE-188 DE-521 |
| physical | xv, 276 Seiten Diagramme |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Probability and its applications |
| spellingShingle | Chung, Kai Lai 1917-2009 Williams, Ruth J. 1955- Introduction to stochastic integration Intégrales stochastiques Intégrales stochastiques ram Martingales (Mathématiques) Martingales (Mathématiques) ram Stochastische integratie gtt Martingales (Mathematics) Stochastic integrals Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4126466-6 (DE-588)4151278-9 |
| title | Introduction to stochastic integration |
| title_auth | Introduction to stochastic integration |
| title_exact_search | Introduction to stochastic integration |
| title_full | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_fullStr | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_full_unstemmed | Introduction to stochastic integration K. L. Chung ; R. J. Williams |
| title_short | Introduction to stochastic integration |
| title_sort | introduction to stochastic integration |
| topic | Intégrales stochastiques Intégrales stochastiques ram Martingales (Mathématiques) Martingales (Mathématiques) ram Stochastische integratie gtt Martingales (Mathematics) Stochastic integrals Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Intégrales stochastiques Martingales (Mathématiques) Stochastische integratie Martingales (Mathematics) Stochastic integrals Stochastisches Integral Martingal Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002614534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chungkailai introductiontostochasticintegration AT williamsruthj introductiontostochasticintegration |