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Nonlinear expectations and stochasti...

Peng, Shige.

Nonlinear expectations and stochastic calculus under uncertaintywith robust CLT and G-Brownian motion /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlinear expectations and stochastic calculus under uncertaintyby Shige Peng.
其他題名:	with robust CLT and G-Brownian motion /
作者:	Peng, Shige.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2019.
面頁冊數:	xiii, 212 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Brownian motion processes.
電子資源:	https://doi.org/10.1007/978-3-662-59903-7
ISBN:	9783662599037$q(electronic bk.)

Nonlinear expectations and stochastic calculus under uncertaintywith robust CLT and G-Brownian motion /
Peng, Shige.

Nonlinear expectations and stochastic calculus under uncertaintywith robust CLT and G-Brownian motion /[electronic resource] :by Shige Peng. - Berlin, Heidelberg :Springer Berlin Heidelberg :2019. - xiii, 212 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.952199-3130 ;. - Probability theory and stochastic modelling ;v.70..

Sublinear Expectations and Risk Measures -- Law of Large Numbers and Central Limit Theorem under Uncertainty -- G-Brownian Motion and Ito'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 Ito'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.

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.

ISBN: 9783662599037$q(electronic bk.)

Standard No.: 10.1007/978-3-662-59903-7doiSubjects--Topical Terms:

183837
Brownian motion processes.

LC Class. No.: QA274.75 / .P464 2019

Dewey Class. No.: 519.233

Nonlinear expectations and stochastic calculus under uncertaintywith robust CLT and G-Brownian motion /
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520 $a 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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