G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type
| dc.creator | Peng, Shige | |
| dc.date | 2006-01-03 | |
| dc.date | 2006-12-31 | |
| dc.date.accessioned | 2026-07-07T07:37:34Z | |
| dc.date.available | 2026-07-07T07:37:34Z | |
| dc.description | 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. | |
| dc.description | Submited to Proceedings Abel Symposium 2005, Dedicated to Professor Kiyosi Ito for His 90th Birthday | |
| dc.identifier | https://arxiv.org/abs/math/0601035 | |
| dc.identifier | http://arxiv.org/abs/math/0601035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120821 | |
| dc.subject | Probability | |
| dc.subject | 60H10, 60H05, 60H30, 60J60, 60J65, 60A05, 60E05, 60G05, 60G51, 35K55, 35K15, 49L25 | |
| dc.title | G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type | |
| dc.type | text |