Stochastic Differential Equations

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Beschreibung

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.

From the reviews of the fifth edition:

"This is a highly readable and refreshingly rigorous introduction to stochastic calculus. This is not a watered-down treatment. It is a serious introduction that starts with fundamental measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several examples of applications. This is the best single resource for learning the stochastic calculus ." (riskbook.com, 2002)

From the reviews of the sixth edition:

"The book has evolved from a 200-page typewritten booklet to a modern classic. Part of its charm and success is the fact that the author does not bother too much with the (for the novice) cumbersome rigorous theory . This does not mean that the book is not rigorous, it is just the timing and dosage of mathematical rigour that is palatable for undergraduates . a highly readable account, suitable for self-study and for use in the classroom." (René L. Schilling, The Mathematical Gazette, March, 2005)

"This is the sixth edition of the classical and excellent book on stochastic differential equations. The main difference with the next to last edition is the addition of detailed solutions of selected exercises . This is certainly an excellent idea in view to test its ability of applications of the concepts . certainly one of the best books on the subject, it will be very helpful to any graduate students and also very valuable for any analysts of financial market." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004)

"This is now the sixth edition of the excellent book on stochastic differential equations and related topics. the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003)



Zusammenfassung

From the reviews of the fifth edition:

"This is a highly readable and refreshingly rigorous introduction to stochastic calculus. ... This is not a watered-down treatment. It is a serious introduction that starts with fundamental measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several examples of applications. This is the best single resource for learning the stochastic calculus ... ." (riskbook.com, 2002)

From the reviews of the sixth edition:

"The book ... has evolved from a 200-page typewritten booklet to a modern classic. Part of its charm and success is the fact that the author does not bother too much with the (for the novice) cumbersome rigorous theory ... . This does not mean that the book is not rigorous, it is just the timing and dosage of mathematical rigour ... that is palatable for undergraduates ... . a highly readable account, suitable for self-study and for use in the classroom." (René L. Schilling, The Mathematical Gazette, March, 2005)

"This is the sixth edition of the classical and excellent book on stochastic differential equations. The main difference with the next to last edition is the addition of detailed solutions of selected exercises ... . This is certainly an excellent idea in view to test its ability of applications of the concepts ... . certainly one of the best books on the subject, it will be very helpful to any graduate students and also very valuable for any analysts of financial market." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004)

"This is now the sixth edition of the excellent book on stochastic differential equations and related topics. ... the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003)



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.

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Produktinformationen

Titel
Stochastic Differential Equations
Untertitel
An Introduction with Applications
Autor
EAN
9783540047582
ISBN
978-3-540-04758-2
Format
Kartonierter Einband
Herausgeber
Springer, Berlin
Genre
Mathematik
Anzahl Seiten
379
Gewicht
576g
Größe
H24mm x B236mm x T155mm
Jahr
2014
Untertitel
Englisch
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