Abstract
In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itô integrals driven by G-Brownian motion and G-Lévy process. By using the G-Itô formula and the properties of G-expectation, two main theorems about Itô integral are obtained and proved. These two theorems provide powerful help for the subsequent research on jump process.
Highlights
In recent years, nonlinear expectation theory has been applied more and more widely in the financial field
In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itô integrals driven by G-Brownian motion and G-Lévy process
Peng [3] studied the existence and uniqueness of solutions of stochastic differential equations driven by G-Brownian motion under Lipschitz condition
Summary
Nonlinear expectation theory has been applied more and more widely in the financial field. In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itô integrals driven by G-Brownian motion and G-Lévy process. By using the G-Itô formula and the properties of G-expectation, two main theorems about Itô integral are obtained and proved.
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