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 in order to quickly progress to the parts of the theory that are 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 well-established textbook on stochastic differential equations has turned out to be very useful to non-specialists of the subject and has sold steadily in 5 editions, both in the EU and US market Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
Some Mathematical Preliminaries.- Itô Integrals.- The 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.- Application to Optimal Stopping.- Application to Stochastic Control.- Application to Mathematical Finance.