Stochastic calculus of variations for jump processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2013
|
| Series: | De Gruyter studies in mathematics
54 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Weitere Ausg.: Online-Ausg. |
| Physical Description: | VIII, 266 S. 240 mm x 170 mm |
| ISBN: | 9783110281804 |
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MARC
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Record in the Search Index
| _version_ | 1806325070929330176 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
PREFACE V
0 INTRODUCTION 1
1 LEVY PROCESSES AND LTD CALCULUS - 5
1.1 POISSON RANDOM MEASURE AND LEVY PROCESSES 5
1.1.1 LEVY PROCESSES 5
1.1.2 EXAMPLES OF LEVY PROCESSES 8
1.1.3 STOCHASTIC INTEGRAL FOR A FINITE VARIATION PROCESS 11
1.2 BASIC MATERIALS TO 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 21
1.3 LTD PROCESSES WITH JUMPS 2 4
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) 59
2.2.1 MARKOV CHAIN APPROXIMATION 59
2.2.2 PROOF OF THEOREM 2.3 63
2.2.3 PROOF OF LEMMAS 70
2.3 METHODS OF FINDING THE ASYMPTOTIC BOUNDS (II) 77
2.3.1 POLYGONAL GEOMETRY 77
2.3.2 PROOF OF THEOREM 2.4 78
2.3.3 EXAMPLE OF THEOREM 2.4 - EASY CASES 8 8
2.4 SUMMARY OF SHORT TIME ASYMPTOTIC BOUNDS 9 6
2.4.1 CASE THAT N ( D Z ) IS ABSOLUTELY CONTINUOUS WITH RESPECT TO THE
M-DIMENSIONAL LEBESGUE MEASURE D Z 9 6 2.4.2 CASE THAT F J ( D Z ) IS
SINGULAR WITH RESPECT TO D Z ' * - 97
2.5 AUXILIARY TOPICS 9 9
2.5.1 MARCUS'CANONICAL PROCESSES 9 9
2.5.2 ABSOLUTE CONTINUITY OF THE INFINITELY DIVISIBLE LAWS 102
2.5.3 CHAIN MOVEMENT APPROXIMATION -- 107
2.5.4 SUPPORT THEOREM FOR CANONICAL PROCESSES 109
HTTP://D-NB.INFO/1030086176
IMAGE 2
VIII - CONTENTS
3 ANALYSIS OFWIENER-POISSON FUNCTIONALS - 114
3.1 CALCULUS OF FUNCTIONALS ON THE WIENER SPACE 114
3.1.1 DEFINITION OF THE MALLIAVIN-SHIGEKAWA DERIVATIVE D T 116
3.1.2 ADJOINT OPERATOR 5 = D * 120
3.2 CALCULUS OF FUNCTIONALS ON THE POISSON SPACE 122
3.2.1 ONE-DIMENSIONAL CASE 122
3.2.2 MULTIDIMENSIONAL CASE 125
3.2.3 CHARACTERISATION OF THE POISSON SPACE 128
3.3 SOBOLEV SPACE FOR FUNCTIONALS OVER THE WIENER-POISSON SPACE - 132
3.3.1 THE WIENER SPACE 132
3.3.2 THE POISSON SPACE 134
3.3.3 THE WIENER-POISSON SPACE 139
3.4 RELATION WITH THE MALLIAVIN OPERATOR 148
3.5 COMPOSITION ON THE WIENER-POISSON SPACE (1) - GENERAL THEORY - 150
3.5.1 COMPOSITION WITH AN ELEMENT IN S' 150
3.5.2 SUFFICIENT CONDITION FOR THE COMPOSITION 156
3.6 SMOOTHNESS OF THE DENSITY FOR ITO PROCESSES 160
3.6.1 PRELIMINARIES 160
3.6.2 BIG PERTURBATIONS 163
3.6.3 CONCATENATION (1) 167
3.6.4 CONCATENATION (II) - THE CASE THAT (D) MAY FAIL 170
3.7 COMPOSITION ON THE WIENER-POISSON SPACE (II) - ITO PROCESSES 178
4 APPLICATIONS - 181
4.1 ASYMPTOTIC EXPANSION OF THE SDE 182
4.1.1 ANALYSIS ON THE STOCHASTIC MODEL 184
4.1.2 ASYMPTOTIC EXPANSION OF THE DENSITY-- 205 4.1.3 EXAMPLES OF
ASYMPTOTIC EXPANSIONS - - 210 4.2 OPTIMAL CONSUMPTION PROBLEM 216
4.2.1 SETTING OF THE OPTIMAL CONSUMPTION - - 216 4.2.2 VISCOSITY
SOLUTIONS 220
4.2.3 REGULARITY OF SOLUTIONS 239
4.2.4 OPTIMAL CONSUMPTION 243
4.2.5 HISTORICAL SKETCH 246
APPENDIX 249
BIBLIOGRAPHY 253
LIST OF SYMBOLS 263
INDEX 264 |
| 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 | BV041089178 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)854727771 (DE-599)DNB1030086176 |
| dewey-full | 519.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.22 |
| dewey-search | 519.22 |
| dewey-sort | 3519.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041089178 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T00:43:46Z |
| institution | BVB |
| isbn | 9783110281804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026065800 |
| oclc_num | 854727771 |
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| owner | DE-29T DE-824 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-29T DE-824 DE-19 DE-BY-UBM DE-11 |
| physical | VIII, 266 S. 240 mm x 170 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| 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 Berlin [u.a.] de Gruyter 2013 VIII, 266 S. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 54 Weitere Ausg.: Online-Ausg. 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 978-3-11-028200-9 De Gruyter studies in mathematics 54 (DE-604)BV000005407 54 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4240948&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026065800&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 for jump processes |
| title_sort | stochastic calculus of variations for jump processes |
| topic | Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| topic_facet | Malliavin-Kalkül Sprungprozess |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4240948&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026065800&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT ishikawayasushi stochasticcalculusofvariationsforjumpprocesses |