Shige Peng
Published 2006-01-03, updated 2006-12-31Version 2
We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with 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 Ito's type with respect to our G--Brownian motion and derive the related Ito's formula. We have also give 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 not based on a given (linear) probability space.
Comments: Submited to Proceedings Abel Symposium 2005, Dedicated to Professor Kiyosi Ito for His 90th Birthday
Subjects: 60H10,
60H05,
60H30,
60J60,
60J65,
60A05,
60E05,
60G05,
60G51,
35K55,
35K15,
49L25
Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation
Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion
On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion
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