| 書目名稱 | Stochastic Analysis | | 編輯 | Shigeo Kusuoka | | 視頻video | http://file.papertrans.cn/878/877816/877816.mp4 | | 概述 | Defines conditional exceptions differently than in other books.Uses only elementary facts for proof of the Doob–Meyer decomposition theorem for special cases.Shows how the Euler–Maruyama approximation | | 叢書名稱 | Monographs in Mathematical Economics | | 圖書封面 |  | | 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 ofthe 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 | | 出版日期 | Book 2020 | | 關(guān)鍵詞 | Martingale for Continuous Time Parameters; Stochastic Integrals; Brownian Motions; Stochastic Different | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-15-8864-8 | | isbn_softcover | 978-981-15-8866-2 | | isbn_ebook | 978-981-15-8864-8Series ISSN 2364-8279 Series E-ISSN 2364-8287 | | issn_series | 2364-8279 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
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