CLT
law
representation theorem
lecture notes
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number
basic definitions
integrals
limit theorem
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https://doi.org/10.1007/978-3-662-59903-7
nonlinear expectations
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graduate textbook
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materials
2022-08-04T17:13
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2019
finance
G-Brownian Motion
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risk
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 Pengâ€™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.
central limit theorem
978-3-662-59902-0
reference
measures
development
students
notion
problem
University
https://scigraph.springernature.com/explorer/license/
Nonlinear Expectations and Stochastic Calculus under Uncertainty, with Robust CLT and G-Brownian Motion
motion
G-expectation
stochastic analysis
end
textbooks
process
results
relation
Brownian motion
theorem
uncertainty
model uncertainty
integrable processes
expectations
calculus
mathematical finance
analysis
topic
book
978-3-662-59903-7
coherent measures
lectures
sublinear expectations
stochastic calculus
monograph
summer school
schools
definition
large number
example
probability theory
true
further references
researchers
coverage
normal distribution
chapter
exercise
recent developments
series
books
note
2019-01-01
10.1007/978-3-662-59903-7
doi
Shige
Peng
Springer Nature
Mathematical Sciences
Statistics
pub.1120936153
dimensions_id
Applied Mathematics
Springer Nature - SN SciGraph project
Institute of Mathematics, Shandong University, Jinan, Shandong, China
Institute of Mathematics, Shandong University, Jinan, Shandong, China