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Peter E. Kloeden, Eckhard Platen
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
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.
David S. Ebert
Congratulations to Ken Perlin for his 1997 Technical Achievement Award from the Academy of Motion Picture Arts and Science Board of Governors, given in recognition of the development of "Turbulence", Perlin Noise, a technique discussed in this book which is used to produce natural appearing textures on computer-generated surfaces for motion picture visual effects. Dr. Perlin joins Darwyn Peachey (co-developer of RenderMan(R), also discussed in the book) in being honored with this prestigious award. * * Written at a usable level by the developers of the techniques * Serves as a source book for those writing rendering systems, shaders, and animations. * Discusses the design and implementation of noise functions. * Contains procedural modeling of gases, hypertextures, mountains, and landscapes. * Provides a toolbox of specific procedures and basic primitive functions for producing realistic images. * Procedures are presented in C code segments or in Renderman shading language. * 3.5" disk contains the code from within the book for easy implementation