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Probability Theory and Stochastic Modelling

Nonlinear Expectations and Stochastic Calculus under Uncertainty

with Robust CLT and G-Brownian Motion

Authors: Peng, Shige

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  • Provides new notions and results of the theory of nonlinear expectations and related stochastic analysis
  • Summarizes the latest studies on G-Martingale representation theorem and Itô’s integrals
  • Includes exercises that help reader master and learn in each chapter
  •  
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書籍の購入

イーブック ¥6,738
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-662-59903-7
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ハードカバー ¥11,933
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-662-59902-0
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
この書籍について

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.

著者について

Shige Peng received his PhD in 1985 at Université Paris-Dauphine, in the direction of mathematics and informatics, and 1986 at University of Provence, in the direction of applied mathematics. He now is a full professor in Shandong University. His main research interests are stochastic optimal controls, backward SDEs and the corresponding PDEs, stochastic HJB equations. He has received the Natural Science Prize of China (1995), Su Buqing Prize of Applied Mathematics (2006), TAN Kah Kee Science Award (2008), Loo-Keng Hua Mathematics Award (2011), and the Qiu Shi Award for Outstanding Scientists (2016).

Table of contents (8 chapters)

Table of contents (8 chapters)

書籍の購入

イーブック ¥6,738
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-662-59903-7
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ハードカバー ¥11,933
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-662-59902-0
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
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書誌情報

Bibliographic Information
Book Title
Nonlinear Expectations and Stochastic Calculus under Uncertainty
Book Subtitle
with Robust CLT and G-Brownian Motion
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
95
Copyright
2019
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Germany, part of Springer Nature
イーブック ISBN
978-3-662-59903-7
DOI
10.1007/978-3-662-59903-7
ハードカバー ISBN
978-3-662-59902-0
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XIII, 212
Number of Illustrations
10 b/w illustrations
Topics