G- Brownian motion and Its Applications

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Abstract. The concept of G-Brownian motion and G-Ito integral has been introduced by Peng. Also Ito isometry lemma is proved for Ito integral and Brownian motion. In this paper we first investigate the Ito isometry lemma for G-Brownian motion and G-Ito Integral. Then after studying of MG2,0-class functions [4], we introduce Stratonovich integral for G-Brownian motion,say G- Stratonovich integral. Then we present a special construction for G- Stratonovich integral. 


G-expectation, G-Brownianmotion, Characterization, Ito integral, G-Stratonovich

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