Description: 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.
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End Time: 2025-01-26T07:20:14.000Z
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EAN: 9783662599051
UPC: 9783662599051
ISBN: 9783662599051
MPN: N/A
Item Length: 23.4 cm
Number of Pages: 212 Pages
Language: English
Publication Name: Nonlinear Expectations and Stochastic Calculus under Uncertainty: with Robust CLT and G-Brownian Motion
Publisher: Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG
Publication Year: 2020
Subject: Accounting, Mathematics
Item Height: 235 mm
Item Weight: 355 g
Type: Textbook
Author: Shige Peng
Series: Probability Theory and Stochastic Modelling
Item Width: 155 mm
Format: Paperback
