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- 题名/责任者:
- Stochastic calculus : an introduction through theory and exercises / Paolo Baldi.
- 出版发行项:
- Cham, Switzerland : Springer, ?2017.
- ISBN:
- 9783319622255
- ISBN:
- 3319622250
- 载体形态项:
- xiv, 627 p. : illustrations (some color) ; 24 cm.
- 丛编说明:
- Universitext, 0172-5939.
- 丛编统一题名:
- Universitext,
- 个人责任者:
- Baldi, Paolo, 1948-
- 论题主题:
- Stochastic analysis.
- 论题主题:
- Stochastic processes.
- 中图法分类号:
- O211.6
- 书目附注:
- Includes bibliographical references (pages 623-624) and index.
- 内容附注:
- 1 Elements of probability -- 2 Stochastic processes -- 3 Brownian motion -- 4 Conditional probability -- 5 Martingales -- 6 Markov Processes -- 7 The stochastic integral -- 8 Stochastic calculus -- 9 Stochastic Differential Equations -- 10 PDE problems and diffusions -- 11 *Simulation -- 12 Back to stochastic calculus -- 13 An application: finance -- Solutions of the exercises -- References -- Index.
- 摘要附注:
- This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.
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