<電子ブック>
Nonlinear Expectations and Stochastic Calculus under Uncertainty : with Robust CLT and G-Brownian Motion / by Shige Peng
(Probability Theory and Stochastic Modelling. ISSN:21993149 ; 95)
版 | 1st ed. 2019. |
---|---|
出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2019 |
本文言語 | 英語 |
大きさ | XIII, 212 p. 10 illus : online resource |
著者標目 | *Peng, Shige author SpringerLink (Online service) |
件 名 | LCSH:Probabilities LCSH:Social sciences -- Mathematics 全ての件名で検索 FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance |
一般注記 | Sublinear Expectations and Risk Measures -- Law of Large Numbers and Central Limit Theorem under Uncertainty -- G-Brownian Motion and Itô’s Calculus -- G-Martingales and Jensen’s Inequality -- Stochastic Differential Equations -- Capacity and Quasi-Surely Analysis for G-Brownian Paths -- G-Martingale Representation Theorem -- Some Further Results of Itô’s Calculus -- Appendix A Preliminaries in Functional Analysis -- Appendix B Preliminaries in Probability Theory -- Appendix C Solutions of Parabolic Partial Differential Equation -- Bibliography -- Index of Symbols -- Subject Index -- Author Index This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful HTTP:URL=https://doi.org/10.1007/978-3-662-59903-7 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9783662599037 |
|
電子リソース |
|
EB00223878 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000134522 |
ISBN | 9783662599037 |
類似資料
この資料の利用統計
このページへのアクセス回数:1回
※2017年9月4日以降