Stochastic Analysis. 1st ed. 2020
- 種類:
- 電子ブック
- 責任表示:
- by Shigeo Kusuoka
- 出版情報:
- Singapore : Springer Nature Singapore : Imprint: Springer, 2020
- 著者名:
- シリーズ名:
- Monographs in Mathematical Economics ; 3
- ISBN:
- 9789811588648 [9811588643]
- 注記:
- 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.
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 - ローカル注記:
- 岐阜大学構成員専用E-BOOKS (Gifu University members only)
類似資料:
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Birkhäuser |
Springer International Publishing : Imprint: Springer |
Birkhäuser Boston |
Scuola Normale Superiore : Imprint: Edizioni della Normale |
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Birkhäuser |
Springer International Publishing : Imprint: Birkhäuser |
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Springer |