{"product_id":"nonlinear-expectations-and-stochastic-calculus-shige-peng-9783662599020","title":"Nonlinear Expectations and Stochastic Calculus Under Uncertainty: With Robust Clt and G-Brownian Motion","description":"\u003cp\u003eThis 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.\u003cbr\u003e\u003c\/p\u003eThis 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 \u003ci\u003eG\u003c\/i\u003e-expectations. It ends with recent research topic on \u003ci\u003eG-\u003c\/i\u003eMartingale representation theorem and \u003ci\u003eG\u003c\/i\u003e-stochastic integral for locally integrable processes.\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWith 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 \u003ci\u003eNotes and Comments, \u003c\/i\u003e which gives history and further references on the material covered in that chapter.\u003c\/p\u003e\u003cp\u003eResearchers and graduate students interested in probability theory and mathematical finance will find this book very useful.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Shige Peng\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3662599023\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783662599020\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/19\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 212\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.10lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.56d","brand":"Shige Peng","offers":[{"title":"Hardcover","offer_id":44073682075903,"sku":"9783662599020","price":129.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_fe2c280e-2d64-423d-9d60-3d7a8d4068ec.jpg?v=1685449277","url":"https:\/\/www.whiterainbookhouse.com\/products\/nonlinear-expectations-and-stochastic-calculus-shige-peng-9783662599020","provider":"WR Book House","version":"1.0","type":"link"}