Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation

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dc.creatorPeng, Shige
dc.date2006-01-28
dc.date2007-01-10
dc.date.accessioned2026-07-07T07:39:25Z
dc.date.available2026-07-07T07:39:25Z
dc.descriptionWe develop a notion of nonlinear expectation --G-expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a multi dimensional 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 obtained the existence and uniqueness of stochastic differential equation under our G-expectation.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0601699
dc.identifierhttp://arxiv.org/abs/math/0601699
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121440
dc.subjectProbability
dc.subject60H10, 60H05, 60H30, 60J60, 60J65
dc.titleMulti-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation
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