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G- Brownian motion and Its Applications

Year 2015, Volume: 36 Issue: 3, 2242 - 2246, 13.05.2015

Atena Ebrahımbeygı Elham Dastranj

Abstract

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. 

Keywords

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

References

  • Oksendal,B.(2003). Stochastic differential equations (pp20-26). Springer Berlin Heidelberg.
  • Peng, S. (2006) G–Expectation, G–Brownian Motion and Related Stochastic Calculus of Itˆo’s type, preprint (pdf-file available in arXiv:math.PR/0601035v1 3Jan 2006), to appear in Proceedings of the 2005, Abel Symposium.
  • Peng, S. (2005), Dynamically consistent nonlinear evaluations and expectations, preprint (pdf-file available in arXiv:math. PR/0501415 v1 24 Jan2005).
  • Peng, S. (2004) Nonlinear expectation, nonlinear evaluations and risk measurs,in K. Back T. R. Bielecki, C. Hipp, S. Peng, W. Schachermayer, Stochastic Methods in Finance Lectures, 143–217, LNM 1856, Springer-Verlag.
  • Peng, S. (2004) Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series 20(2), 1–24.

Year 2015, Volume: 36 Issue: 3, 2242 - 2246, 13.05.2015

Atena Ebrahımbeygı Elham Dastranj

Abstract

References

  • Oksendal,B.(2003). Stochastic differential equations (pp20-26). Springer Berlin Heidelberg.
  • Peng, S. (2006) G–Expectation, G–Brownian Motion and Related Stochastic Calculus of Itˆo’s type, preprint (pdf-file available in arXiv:math.PR/0601035v1 3Jan 2006), to appear in Proceedings of the 2005, Abel Symposium.
  • Peng, S. (2005), Dynamically consistent nonlinear evaluations and expectations, preprint (pdf-file available in arXiv:math. PR/0501415 v1 24 Jan2005).
  • Peng, S. (2004) Nonlinear expectation, nonlinear evaluations and risk measurs,in K. Back T. R. Bielecki, C. Hipp, S. Peng, W. Schachermayer, Stochastic Methods in Finance Lectures, 143–217, LNM 1856, Springer-Verlag.
  • Peng, S. (2004) Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series 20(2), 1–24.
There are 5 citations in total.

Details

Journal Section Special
Authors

Atena Ebrahımbeygı

Elham Dastranj This is me

Publication Date May 13, 2015
Published in Issue Year 2015 Volume: 36 Issue: 3

Cite

APA Ebrahımbeygı, A., & Dastranj, E. (2015). G- Brownian motion and Its Applications. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(3), 2242-2246.
AMA Ebrahımbeygı A, Dastranj E. G- Brownian motion and Its Applications. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. May 2015;36(3):2242-2246.
Chicago Ebrahımbeygı, Atena, and Elham Dastranj. “G- Brownian Motion and Its Applications”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 3 (May 2015): 2242-46.
EndNote Ebrahımbeygı A, Dastranj E (May 1, 2015) G- Brownian motion and Its Applications. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 3 2242–2246.
IEEE A. Ebrahımbeygı and E. Dastranj, “G- Brownian motion and Its Applications”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, pp. 2242–2246, 2015.
ISNAD Ebrahımbeygı, Atena - Dastranj, Elham. “G- Brownian Motion and Its Applications”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/3 (May 2015), 2242-2246.
JAMA Ebrahımbeygı A, Dastranj E. G- Brownian motion and Its Applications. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:2242–2246.
MLA Ebrahımbeygı, Atena and Elham Dastranj. “G- Brownian Motion and Its Applications”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, 2015, pp. 2242-6.
Vancouver Ebrahımbeygı A, Dastranj E. G- Brownian motion and Its Applications. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(3):2242-6.