Stochastic Differential Equations
An Introduction with Applications
(Sprache: Englisch)
This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed in the...
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This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed in the end of each chapter, in order to facilitate the use of this edition together with previous ones. Several errors have been corrected and formulations have been improved. This has been made possible by the valuable comments from (in alphabetical order) Jon Bohlin, Mark Davis, Helge Holden, Patrick Jaillet, Chen Jing, Natalia Koroleva,MarioLefebvre,Alexander Matasov,Thilo Meyer-Brandis, Keigo Osawa, Bjørn Thunestvedt, Jan Ubøe and Yngve Williassen. I thank them all for helping to improve the book. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the ?gures with great skill. Blindern, September 2002 Bernt Øksendal xv Preface to Corrected Printing, Fifth Edition The main corrections and improvements in this corrected printing are from Chapter 12. I have bene?tted from useful comments from a number of p- ple, including (in alphabetical order) Fredrik Dahl, Simone Deparis, Ulrich Haussmann, Yaozhong Hu, Marianne Huebner, Carl Peter Kirkebø, Ni- lay Kolev, Takashi Kumagai, Shlomo Levental, Geir Magnussen, Anders Øksendal, Jur gen Pottho?, Colin Rowat, Stig Sandnes, Lones Smith, S- suo Taniguchi and Bjørn Thunestvedt. I want to thank them all for helping me making the book better. I also want to thank Dina Haraldsson for pro?cient typing.
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.
This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.
This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.
Inhaltsverzeichnis zu „Stochastic Differential Equations “
- Introduction- Some Mathematical Preliminaries
- Itô Integrals
- Itô Formula and the Martingale Representation Theorem
- Stochastic Differential Equations
- The Filtering Problem
- Diffusions: Basic Properties
- Other Topics in Diffusion Theory
- Applications to Boundary Value Problems
- Applications to Optimal Stopping
- Application to Stochastic Control
- Application to Mathematical Finance
- Appendix A: Normal Random Variables
- Appendix B: Conditional Expectations
- Appendix C: Uniform Integrability and Martingale Convergence
- Appendix D: An Approximation Result
- Solutions and Additional Hints to Some of the Exercises
- References
- List of Frequently Used Notation and Symbols
- Index
Bibliographische Angaben
- Autor: Bernt Øksendal
- 2014, 6th ed., 4th corr. pr., 379 Seiten, 14 Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540047581
- ISBN-13: 9783540047582
- Erscheinungsdatum: 04.02.2014
Sprache:
Englisch
Rezension zu „Stochastic Differential Equations “
Aus den Rezensionen zur 6. Auflage:"Dieser Klassiker ... ist sowohl als Lehrbuch als auch zum Selbststudium hervorragend geeignet. Ausgehend von sechs Problemstellungen ... wird in gut verständlicher Weise ... die Theorie stochastischer Differentialgleichungen entwickelt. ... Am Ende eines jeden Kapitels sind zahlreiche Übungsbeispiele zu finden. Die vorliegende 6. Auflage unterscheidet sich von der vorigen vor allem durch zusätzliche Übungsbeispiele sowie Lösungshinweise zu einer Auswahl davon. ... Mittlerweile ist das Buch auch in elektronischer Form als e-book beim Verlag erhältlich."(H. Albrecher, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 203, S. 36)
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