Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 95)
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About this book
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.
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.
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Keywords
- probability theory
- stochastic analysis
- uncertainty of probabilities
- nonlinear expectations
- independence and identical distribution under uncertainty
- law of large numbers
- central limit theorem
- maximal distribution
- G-normal distribution
- G-Brownian motion
- G-martingale
- G-martingale representation theorem
- stochastic integral of G-Brownian motion
- stochastic differential equations driven by G-Brownian motion
- quadratic variation process of G-Brownian motion
- nonlinear Feynman-Kac formula
- mathematical statistics
- quantitative finance
Table of contents (8 chapters)
-
Basic Theory of Nonlinear Expectations
-
Stochastic Analysis Under G-Expectations
-
Stochastic Calculus for General Situations
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Bibliographic Information
Book Title: Nonlinear Expectations and Stochastic Calculus under Uncertainty
Book Subtitle: with Robust CLT and G-Brownian Motion
Authors: Shige Peng
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-662-59903-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2019
Hardcover ISBN: 978-3-662-59902-0Published: 19 September 2019
Softcover ISBN: 978-3-662-59905-1Published: 19 September 2020
eBook ISBN: 978-3-662-59903-7Published: 09 September 2019
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XIII, 212
Number of Illustrations: 10 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Quantitative Finance