Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
AbstractWe 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 Itô's type with respect to our G-Brownian motion, and derive the related Itô's formula. We have also obtained the existence and uniqueness of stochastic differential equations under our G-expectation.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 118 (2008)
Issue (Month): 12 (December)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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