Multi-Dimensional G–Brownian Motion and Related Stochastic Calculus under G–Expectation
نویسنده
چکیده
We 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 equation under our G–expectation.
منابع مشابه
G–Expectation, G–Brownian Motion and Related Stochastic Calculus of Itô Type
We introduce a notion of nonlinear expectation —-G–expectation—generated by a nonlinear heat equation with a given 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 stoc...
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