标题:G-expectation, G-Brownian motion and related Stochastic calculus of ito type
作者:Peng, Shige
通讯作者:Peng, S
作者机构:[Peng, S]Shandong Univ, Inst Math, Inst Finance, Jinan 250100, Peoples R China.
会议名称:2nd Abel Symposium held in Honor of Kiyosi Ito
会议日期:JUL 29-AUG 04, 2005
来源:Stochastic Analysis and Applications
出版年:2007
卷:2
页码:541-567
关键词:g-expectation; G-expectation; G-normal distribution; BSDE; SDE;; nonlinear probability theory; nonlinear expectation; Brownian motion;; Ito's stochastic calculus; lto's integral; Ito's formula; Gaussian; process; quadratic variation process
摘要:We introduce a notion of nonlinear expectation - G-expectation generated by a nonlinear heat equation with a given infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of lto's type with respect to our G-Brownian motion and derive the related Ito's formula. We have also given the existence and uniqueness of stochastic differential equation under our G-expectation. As compared with our previous framework of g-expectations, the theory of G-expectation is intrinsic in the sense that it is Dot based on a given (linear) probability space.
收录类别:CPCI-S
WOS核心被引频次:105
资源类型:会议论文
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