Extension and Application of Itô's Formula UnderG-Framework

A note on the stochastic differential equations driven by -Brownian motion

“…For the properties of the extended Itô integral, one can see Zhang et al (2010) and the references therein.…”

“…For more details, one can see Bai and Lin (2010), Peng (2007b), Zhang et al (2010) and the references therein. • Let Ω denote the space of all R n -valued continuous functions with ω 0 = 0, equipped with the distance…”

“…Since then, many works have been done on the stochastic calculus with respect to the G-Brownian motion. One can see Denis et al (2008), Hu and Peng (2009), Peng (2008Peng ( , 2007b, Xu and Zhang (2009) and Zhang et al (2010). Very recently, Gao (2009) proved the existence and uniqueness of the solution of stochastic differential equations driven by G-Brownian motion (GSDEs, for short) with Lipschitzian coefficients.…”

Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

“…Under the G-framework, Peng (2006Peng ( , 2010 introduced the socalled G-Gaussian distribution and the G-Brownian motion and used them to set up the associated Itô integral. Since then, many works have been carried out on the stochastic calculus with respect to the G-Brownian motion, see for example Chen et al (2013), Denis et al (2011), Hu and, Hu et al (2012), Peng (2009), Lin (2013), Lin and Bai (2010), Ren et al (2013), Song (2012), Zhang (2009), andZhang et al (2010). Recently, Gao (2009) proved the existence and uniqueness of the solution of SDEs driven by G-Brownian motion (G-SDEs) with Lipschitzian coefficients.…”

General Martingale Characterization ofG-Brownian Motion

“…Moreover, Peng [7,10,12] developed an Itô calculus for the G-Brownian motion. Peng [7,10,12] and Zhang et al [18] established Itô's formula for the G-Brownian motion.…”