Stochastic calculus of variations: for jump processes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2016]
|
| Edition: | 2nd edition |
| Series: | De Gruyter studies in mathematics
volume 54 |
| Subjects: | |
| Online Access: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110377767&searchTitles=true Inhaltsverzeichnis |
| Physical Description: | X, 278 Seiten |
| ISBN: | 9783110377767 9783110378085 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic calculus of variations |b for jump processes |c Yasushi Ishikawa |
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| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2016] | |
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Record in the Search Index
| _version_ | 1804176086298263552 |
|---|---|
| adam_text | CONTENTS
PREFACE * V
PREFACE TO THE SECOND EDITION * VN
0 INTRODUCTION * 1
1 LEVY PROCESSES AND ITO CALCULUS
*
5
1.1 POISSON RANDOM MEASURE AND LEVY PROCESSES * 5
1.1.1 LEVYPROCESSES * 5
1.1.2 EXAMPLES OF L*VY PROCESSES**8
1.1.3 STOCHASTIC INTEGRAL FOR A FINITE VARIATION PROCESS * 11
19
BASIC MATERIALS FOR SDES WITH JUMPS * 13
1.2.1 MARTINGALES AND SEMIMARTINGALES * 13
1.2.2 STOCHASTIC INTEGRAL WITH RESPECT TO SEMIMARTINGALES * 15
1.2.3 DOLEANS* EXPONENTIAL AND GIRSANOV TRANSFORMATION * * 22
1.3 ITO PROCESSES WITH JUMPS * 25
2 PERTURBATIONS AND PROPERTIES OF THE PROBABILITY LAW * 33
2.1 INTEGRATION-BY-PARTS ON POISSON SPACE * 33
2.1.1 BISMUT*S METHOD * 35
2.1.2 PICARD*S METHOD * 45
2.1.3 SOME PREVIOUS METHODS * 51
2.2 METHODS OF FINDING THE ASYMPTOTIC BOUNDS (I)
* 58
2.2.1 MARKOV CHAIN APPROXIMATION * 59
2.2.2 PROOF OF THEOREM 2.3 * 63
2.2.3 PROOF OF LEMMAS * 69
2.3 METHODS OF FINDING THE ASYMPTOTIC BOUNDS (II)
*
75
2.3.1 POLYGONAL GEOMETRY * 76
2.3.2 PROOF OFTHEOREM 2.4 * 77
2.3.3 EXAMPLE OF THEOREM 2.4 - EASY CASES * 87
2.4 SUMMARY OF SHORT TIME ASYMPTOTIC BOUNDS
* 94
2.4.1 CASE THAT
*(DZ) IS ABSOLUTELY CONTINUOUS WITH RESPECT TO THE
.DIM ENSIONA L LEBESGUE MEASURE DZ * 94
2.4.2 CASE THA**(DZ) ISSINGULARWITH RESPECTTODZ * 95
2.5 AUXILIARY TOPICS * 97
2.5.1 MARCUS* CANONICAL PROCESSES _ 97
2.5.2 ABSOLUTE CONTINUITY OF THE INFINITELY DIVISIBLE LAWS * 100
2.5.3 CHAIN MOVEMENT APPROXIMATION** 105
2.5.4 SUPPORT THEOREM FOR CANONICAL PROCESSES * 107
3 ANALYSIS OF WIENER-POISSON FUNCTIONALS ** 111
3.1 CALCULUS OF FUNCTIONALS ON THE WIENER SPACE * 111
3.1.1 DEFINITION OF THE MALLIAVIN-SHIGEKAWA DERIVATIVE 113 *
**
3.1.2 ADJOINT OPERATORS = D* ** 117
3.2 CALCULUS OF FUNCTIONALS ON THE POISSON SPACE * 119
3.2.1 ONE-DIMENSIONAL CASE *
H Q
3.2.2 MULTIDIMENSIONAL CASE * 122
3.2.3 CHARACTERISATION OF THE POISSON SPACE * 125
3.3 SOBOLEV SPACE FOR FUNCTIONALS OVER THE WIENER-POISSON SPACE * 129
3.3.1 THE WIENER SPACE * 129
3.3.2 THE POISSON SPACE * 130
3.3.3 THE WIENER-POISSON SPACE * 137
3.4 RELATION WITH THE MALLIAVIN OPERATOR * 144
3.5 COMPOSITION ON THE WIENER*POISSON SPACE (
*
) * GENERAL THEORY * 146
3.5.1 COMPOSITION WITH AN ELEMENT *N 147*
* *
3.5.2 SUFFICIENT CONDITION FOR THE COMPOSITION * 153
3.6 SMOOTHNESS OF THE DENSITY FOR *TO PROCESSES * 158
3.6.1 PRELIMINARIES * 158
3.6.2 BIG PERTURBATIONS * 161
3.6.3 CONCATENATION (I)
*
165
3.6.4 CONCATENATION (II) - THE CASE THAT (D) MAY FAIL * 172
3.6.5 MORE ON THE DENSITY* 178
3.7 COMPOSITION ON THE WIENER*POISSON SPACE (M)
*
ITO PROCESSES * 192
4 APPLICATIONS * 195
4.1 ASYMPTOTIC EXPANSION OF THE SDE * 195
4.1.1 ANALYSIS ON THE STOCHASTIC MODEL * 198
4.1.2 ASYMPTOTIC EXPANSION OF THE DENSITY** 219
4.1.3 EXAMPLES OF ASYMPTOTIC EXPANSIONS * 223
4.2 OPTIMAL CONSUMPTION PROBLEM * 229
4.2.1 SETTING OF THE OPTIMAL CONSUMPTION * 229
4.2.2 VISCOSITY SOLUTIONS * 232
4.2.3 REGULARITY OF SOLUTIONS
*
251
4.2.4 OPTIMAL CONSUMPTION * 255
4.2.5 HISTORICAL SKETCH * 258
APPENDIX * 261
BIBLIOGRAPHY * 265
LIST OF SYMBOLS * 275
INDEX * 277
|
| any_adam_object | 1 |
| author | Ishikawa, Yasushi 1959- |
| author_GND | (DE-588)1036467341 |
| author_facet | Ishikawa, Yasushi 1959- |
| author_role | aut |
| author_sort | Ishikawa, Yasushi 1959- |
| author_variant | y i yi |
| building | Verbundindex |
| bvnumber | BV043469128 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)921524926 (DE-599)DNB1076283209 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd edition |
| format | Book |
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| id | DE-604.BV043469128 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:26:35Z |
| institution | BVB |
| isbn | 9783110377767 9783110378085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028886183 |
| oclc_num | 921524926 |
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| owner | DE-29T DE-11 DE-19 DE-BY-UBM DE-703 DE-83 |
| owner_facet | DE-29T DE-11 DE-19 DE-BY-UBM DE-703 DE-83 |
| physical | X, 278 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Ishikawa, Yasushi 1959- Verfasser (DE-588)1036467341 aut Stochastic calculus of variations for jump processes Yasushi Ishikawa 2nd edition Berlin ; Boston De Gruyter [2016] © 2016 X, 278 Seiten txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics volume 54 Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Sprungprozess (DE-588)4427906-1 gnd rswk-swf Sprungprozess (DE-588)4427906-1 s Malliavin-Kalkül (DE-588)4242584-0 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-039232-6 Erscheint auch als Online-Ausgabe, PDF 978-3-11-037807-8 De Gruyter studies in mathematics volume 54 (DE-604)BV000005407 54 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110377767&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028886183&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ishikawa, Yasushi 1959- Stochastic calculus of variations for jump processes De Gruyter studies in mathematics Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| subject_GND | (DE-588)4242584-0 (DE-588)4427906-1 |
| title | Stochastic calculus of variations for jump processes |
| title_auth | Stochastic calculus of variations for jump processes |
| title_exact_search | Stochastic calculus of variations for jump processes |
| title_full | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_fullStr | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_full_unstemmed | Stochastic calculus of variations for jump processes Yasushi Ishikawa |
| title_short | Stochastic calculus of variations |
| title_sort | stochastic calculus of variations for jump processes |
| title_sub | for jump processes |
| topic | Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| topic_facet | Malliavin-Kalkül Sprungprozess |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110377767&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028886183&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT ishikawayasushi stochasticcalculusofvariationsforjumpprocesses |