E-Book, Englisch, 208 Seiten, Web PDF
Metivier / Pellaumail / Birnbaum Stochastic Integration
1. Auflage 2014
ISBN: 978-1-4832-1878-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 208 Seiten, Web PDF
ISBN: 978-1-4832-1878-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Stochastic Integration;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;Acknowledgments;11
7;Notation;12
8;CHAPTER 1. STOCHASTIC INTEGRAL WITH RESPECT TO p-PROCESSES;14
8.1;1 Stochastic Basis and Processes;14
8.2;Extensions and Exercises;29
8.3;2 Stochastic Integral;31
8.4;Extensions and Exercises;45
8.5;Historical Notes;47
9;CHAPTER 2. THE ITO FORMULA;48
9.1;3 Ito Formula;48
9.2;4 Applications of the Ito Formula;63
9.3;Extensions and Exercises;73
9.4;Historical Notes;75
10;CHAPTER 3. STOCHASTIC INTEGRAL EQUATIONS;76
10.1;5 Examples of Stochastic Differential Equations;77
10.2;6 General Stochastic Integral Equations;80
10.3;7 Properties of Solutions; Conditions for Nonexplosion and Stability;96
10.4;Exercises;104
10.5;Historical Notes;105
11;CHAPTER 4. MARTINGALES AND SEMIMARTINGALES;106
11.1;8 Martingales and Submartingales: Equi-Integrability and Tied Properties;106
11.2;Extensions and Exercises;115
11.3;9 Meyer Process and Decomposition Theorem;116
11.4;Extensions and Examples;130
11.5;10 p*-Processes and Semimartingales;131
11.6;Extensions and Examples;143
11.7;11 Inequalities;146
11.8;Historical Notes;157
12;CHAPTER 5. STOCHASTIC MEASURES;159
12.1;12 Stochastic Measures and Related Integration;160
12.2;13 Riesz Representation Theorem;168
12.3;Historical Notes;174
13;CHAPTER 6. SPECIAL FEATURES OF INFINITE-DIMENSIONAL STOCHASTIC INTEGRATION;175
13.1;14 The Isometric Integral of a Hilbert-Valued Square Integrable Martingale;176
13.2;Extensions and Comments;189
13.3;15 Cylindrical Processes;189
13.4;16 Stochastic Integral with Respect to 2-Cylindrical Martingales with Finite Quadratic Variation;194
13.5;Historical Notes;200
14;BIBLIOGRAPHY;201
15;INDEX;208
