Nonlinear Expectations and Stochastic Calculus under Uncertainty
Shige Peng
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Naturwissenschaften, Medizin, Informatik, Technik / Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
Beschreibung
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.
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.
Kundenbewertungen
G-Brownian motion, stochastic differential equations driven by G-Brownian motion, quantitative finance, stochastic analysis, central limit theorem, G-martingale representation theorem, maximal distribution, probability theory, stochastic integral of G-Brownian motion, uncertainty of probabilities, law of large numbers, G-martingale, G-normal distribution, nonlinear Feynman-Kac formula, mathematical statistics, quadratic variation process of G-Brownian motion, nonlinear expectations, independence and identical distribution under uncertainty