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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. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten.
レビュー
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." (Ren 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." (Stphane Mtens, 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)
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19 人中、10人の方が、｢このレビューが参考になった｣と投票しています。
By カスタマー
形式:ペーパーバック
確率論の基礎や伊東積分について明確な説明をしてあり非常に優れている。確率微分方程式の応用例がいくつか解説してある。また数理ファイナンスについても１章をさいてあり、重要な事項は説明されている。 ファイナンシャルエンジニアにとって、確率論の教科書としては非常に優れていると思う。
21 人中、4人の方が、｢このレビューが参考になった｣と投票しています。
By 好運來了
形式:ペーパーバック
１９９９年３月に、日本語版が出版されています。邦題は
「確率微分方程式―入門から応用まで」。
「確率微分方程式―入門から応用まで」。
それでなくても難解な数学的理論の本を無理して英語で
読むこともないかと思います。ちなみに、日本語で読ん
でも、これ単独で中身を理解するのはきついのではないか
と、私は思っています。
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