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Stochastic Analysis (Monographs in Mathematical Economics Book 3) 🔍
Shigeo Kusuoka Springer Singapore : Imprint: Springer, Monographs in Mathematical Economics, Monographs in Mathematical Economics 3, 1, 2020
英语 [en] · EPUB · 26.5MB · 2020 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/upload/zlib · Save
描述
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas.
In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
备用文件名
nexusstc/Stochastic Analysis/352b662ee83ecf5f1813f5ddc988b165.epub
备用文件名
lgli/Stochastic Analysis.epub
备用文件名
lgrsnf/Stochastic Analysis.epub
备用文件名
scihub/10.1007/978-981-15-8864-8.pdf
备用文件名
zlib/Science (General)/Shigeo Kusuoka/Stochastic Analysis_6148151.epub
备选作者
Kusuoka, Shigeo
备用出版商
Springer Nature Singapore Pte Ltd Fka Springer Science + Business Media Singapore Pte Ltd
备用版本
Monographs in Mathematical Economics, 3, 1st ed. 2020, Singapore, 2020
备用版本
Monographs in mathematical economics, volume 3, Singapore, 2020
备用版本
Springer Nature, Singapore, 2020
备用版本
Singapore, Singapore
元数据中的注释
lg2835538
元数据中的注释
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备用描述
Chapter 1. Preparations from probability theory -- Chapter 2. Martingale with discrete parameter -- Chapter 3. Martingale with continuous parameter -- Chapter 4. Stochastic integral -- Chapter 5. Applications of stochastic integral -- Chapter 6. Stochastic differential equation -- Chapter 7. Application to finance -- Chapter 8. Appendices -- References
备用描述
Monographs in Mathematical Economics
Erscheinungsdatum: 20.10.2020
开源日期
2020-11-09
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