Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation

Shige Peng

Stochastic Processes and their Applications, 2008, vol. 118, issue 12, 2223-2253

Abstract: 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 equations under our G-expectation.

Keywords: g-expectation; G-expectation; G-normal; distribution; BSDE; SDE; Nonlinear; probability; theory; Nonlinear; expectation; Brownian; motion; Ito's; stochastic; calculus; Ito's; integral; Ito's; formula; Gaussian; process; Quadratic; variation; process; Jensen's; inequality; G-convexity (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (91)

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