Stochastic calculus of variations for jump processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2013]
|
| Schriftenreihe: | De Gruyter studies in mathematics
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Includes bibliographical references (pages 253-261) and index This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes ""with jumps"" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) ""with jumps"". The book also contains some applications of the stochastic calculus for processes with jumps to the c Preface; 0 Introduction; 1 Lvy processes and It{OCLCbr#99} calculus; 1.1 Poisson random measure and Lvy processes; 1.1.1 Lvy processes; 1.1.2 Examples of Lvy processes; 1.1.3 Stochastic integral for a finite variation process; 1.2 Basic materials to SDEs with jumps; 1.2.1 Martingales and semimartingales; 1.2.2 Stochastic integral with respect to semimartingales; 1.2.3 Dolans' exponential and Girsanov transformation; 1.3 It{OCLCbr#99} processes with jumps; 2 Perturbations and properties of the probability law; 2.1 Integration-by-parts on Poisson space; 2.1.1 Bismut's method; 2.1.2 Picard's method 3.3.3 The Wiener-Poisson space3.4 Relation with the Malliavin operator; 3.5 Composition on the Wiener-Poisson space (I) -- general theory; 3.5.1 Composition with an element in S'; 3.5.2 Sufficient condition for the composition; 3.6 Smoothness of the density for It{OCLCbr#99} processes; 3.6.1 Preliminaries; 3.6.2 Big perturbations; 3.6.3 Concatenation (I); 3.6.4 Concatenation (II) -- the case that (D) may fail; 3.7 Composition on the Wiener-Poisson space (II) -- It{OCLCbr#99} processes; 4 Applications; 4.1 Asymptotic expansion of the SDE; 4.1.1 Analysis on the stochastic model 4.1.2 Asymptotic expansion of the density4.1.3 Examples of asymptotic expansions; 4.2 Optimal consumption problem; 4.2.1 Setting of the optimal consumption; 4.2.2 Viscosity solutions; 4.2.3 Regularity of solutions; 4.2.4 Optimal consumption; 4.2.5 Historical sketch; Appendix; Bibliography; List of symbols; Index |
| Beschreibung: | viii, 266 pages |
| ISBN: | 9783110282009 3110282003 9781299721739 1299721737 9783110282016 3110282011 9783110281804 3110281805 |
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| 245 | 1 | 0 | |a Stochastic calculus of variations for jump processes |c Yasushi Ishikawa |
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| 300 | |a viii, 266 pages | ||
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| 490 | 0 | |a De Gruyter studies in mathematics | |
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| 500 | |a This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes ""with jumps"" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) ""with jumps"". The book also contains some applications of the stochastic calculus for processes with jumps to the c | ||
| 500 | |a Preface; 0 Introduction; 1 Lvy processes and It{OCLCbr#99} calculus; 1.1 Poisson random measure and Lvy processes; 1.1.1 Lvy processes; 1.1.2 Examples of Lvy processes; 1.1.3 Stochastic integral for a finite variation process; 1.2 Basic materials to SDEs with jumps; 1.2.1 Martingales and semimartingales; 1.2.2 Stochastic integral with respect to semimartingales; 1.2.3 Dolans' exponential and Girsanov transformation; 1.3 It{OCLCbr#99} processes with jumps; 2 Perturbations and properties of the probability law; 2.1 Integration-by-parts on Poisson space; 2.1.1 Bismut's method; 2.1.2 Picard's method | ||
| 500 | |a 3.3.3 The Wiener-Poisson space3.4 Relation with the Malliavin operator; 3.5 Composition on the Wiener-Poisson space (I) -- general theory; 3.5.1 Composition with an element in S'; 3.5.2 Sufficient condition for the composition; 3.6 Smoothness of the density for It{OCLCbr#99} processes; 3.6.1 Preliminaries; 3.6.2 Big perturbations; 3.6.3 Concatenation (I); 3.6.4 Concatenation (II) -- the case that (D) may fail; 3.7 Composition on the Wiener-Poisson space (II) -- It{OCLCbr#99} processes; 4 Applications; 4.1 Asymptotic expansion of the SDE; 4.1.1 Analysis on the stochastic model | ||
| 500 | |a 4.1.2 Asymptotic expansion of the density4.1.3 Examples of asymptotic expansions; 4.2 Optimal consumption problem; 4.2.1 Setting of the optimal consumption; 4.2.2 Viscosity solutions; 4.2.3 Regularity of solutions; 4.2.4 Optimal consumption; 4.2.5 Historical sketch; Appendix; Bibliography; List of symbols; Index | ||
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 7 | |a Calculus of variations |2 fast | |
| 650 | 7 | |a Jump processes |2 fast | |
| 650 | 7 | |a Malliavin calculus |2 fast | |
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| 650 | 4 | |a Calculus of variations | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ishikawa, Yasushi 1959 October 1- |
| author_facet | Ishikawa, Yasushi 1959 October 1- |
| author_role | aut |
| author_sort | Ishikawa, Yasushi 1959 October 1- |
| author_variant | y i yi |
| building | Verbundindex |
| bvnumber | BV043776550 |
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| dewey-full | 519.2/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/2 |
| dewey-search | 519.2/2 |
| dewey-sort | 3519.2 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043776550 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:34:48Z |
| institution | BVB |
| isbn | 9783110282009 3110282003 9781299721739 1299721737 9783110282016 3110282011 9783110281804 3110281805 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029187610 |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | viii, 266 pages |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | De Gruyter |
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| series2 | De Gruyter studies in mathematics |
| spelling | Ishikawa, Yasushi 1959 October 1- Verfasser aut Stochastic calculus of variations for jump processes Yasushi Ishikawa Berlin De Gruyter [2013] viii, 266 pages txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics Includes bibliographical references (pages 253-261) and index This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes ""with jumps"" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) ""with jumps"". The book also contains some applications of the stochastic calculus for processes with jumps to the c Preface; 0 Introduction; 1 Lvy processes and It{OCLCbr#99} calculus; 1.1 Poisson random measure and Lvy processes; 1.1.1 Lvy processes; 1.1.2 Examples of Lvy processes; 1.1.3 Stochastic integral for a finite variation process; 1.2 Basic materials to SDEs with jumps; 1.2.1 Martingales and semimartingales; 1.2.2 Stochastic integral with respect to semimartingales; 1.2.3 Dolans' exponential and Girsanov transformation; 1.3 It{OCLCbr#99} processes with jumps; 2 Perturbations and properties of the probability law; 2.1 Integration-by-parts on Poisson space; 2.1.1 Bismut's method; 2.1.2 Picard's method 3.3.3 The Wiener-Poisson space3.4 Relation with the Malliavin operator; 3.5 Composition on the Wiener-Poisson space (I) -- general theory; 3.5.1 Composition with an element in S'; 3.5.2 Sufficient condition for the composition; 3.6 Smoothness of the density for It{OCLCbr#99} processes; 3.6.1 Preliminaries; 3.6.2 Big perturbations; 3.6.3 Concatenation (I); 3.6.4 Concatenation (II) -- the case that (D) may fail; 3.7 Composition on the Wiener-Poisson space (II) -- It{OCLCbr#99} processes; 4 Applications; 4.1 Asymptotic expansion of the SDE; 4.1.1 Analysis on the stochastic model 4.1.2 Asymptotic expansion of the density4.1.3 Examples of asymptotic expansions; 4.2 Optimal consumption problem; 4.2.1 Setting of the optimal consumption; 4.2.2 Viscosity solutions; 4.2.3 Regularity of solutions; 4.2.4 Optimal consumption; 4.2.5 Historical sketch; Appendix; Bibliography; List of symbols; Index MATHEMATICS / Probability & Statistics / General bisacsh Calculus of variations fast Jump processes fast Malliavin calculus fast Malliavin calculus Calculus of variations Jump processes 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 1\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ishikawa, Yasushi 1959 October 1- Stochastic calculus of variations for jump processes MATHEMATICS / Probability & Statistics / General bisacsh Calculus of variations fast Jump processes fast Malliavin calculus fast Malliavin calculus Calculus of variations Jump processes 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 | MATHEMATICS / Probability & Statistics / General bisacsh Calculus of variations fast Jump processes fast Malliavin calculus fast Malliavin calculus Calculus of variations Jump processes Malliavin-Kalkül (DE-588)4242584-0 gnd Sprungprozess (DE-588)4427906-1 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Calculus of variations Jump processes Malliavin calculus Malliavin-Kalkül Sprungprozess |
| work_keys_str_mv | AT ishikawayasushi stochasticcalculusofvariationsforjumpprocesses |