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＜電子ブック＞
Nonlinear Expectations and Stochastic Calculus under Uncertainty : with Robust CLT and G-Brownian Motion / by Shige Peng
(Probability Theory and Stochastic Modelling. ISSN:21993149 ; 95)

版	1st ed. 2019.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	XIII, 212 p. 10 illus : online resource
著者標目	*Peng, Shige author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Social sciences -- Mathematics  全ての件名で検索 FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-59903-7

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