G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type

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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.
Submited to Proceedings Abel Symposium 2005, Dedicated to Professor Kiyosi Ito for His 90th Birthday

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Probability, 60H10, 60H05, 60H30, 60J60, 60J65, 60A05, 60E05, 60G05, 60G51, 35K55, 35K15, 49L25

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http://salesiana.dossiersoluciones.com/handle/123456789/120821

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601035
 http://arxiv.org/abs/math/0601035

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arXiv