Nonlinear Expectations and Stochastic Calculus under Uncertainty with Robust CLT and G-Brownian Motion /

• Main Author: Peng, Shige (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Probability Theory and Stochastic Modelling, 95
• Subjects: Probabilities.; Economics, Mathematical .; Probability Theory and Stochastic Processes.; Quantitative Finance.

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 a...

Table of Contents:

• 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.