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Warianty tytułu
Języki publikacji
Abstrakty
In this paper, we are motivated by uncertainty problems in volatility. We prove the equivalent theorem of Wiener chaos with respect to G-Brownian motion in the framework of a sublinear expectation space. Moreover, we establish some relationship between Hermite polynomials and G-stochastic multiple integrals. An equivalent of the orthogonality of Wiener chaos was found.
Czasopismo
Rocznik
Tom
Strony
647--666
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Laboratoire LaPS, Département de Mathématiques Faculté des Sciences,Université Badji Mokhtar Annaba 23000, Algéria
autor
- Département de Mathématiques, Faculté des Sciences Université Badji Mokhtar-Annaba 23000, Algéria
Bibliografia
- [1] L. Denis, M. Hu, S. Peng, Function spaces and capacity related to a sublinear expectation: Application to G-Brownian motion pathes, Potential Anal. 34 (2011) 2, 139–161.
- [2] L. Denis, C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, Ann. of App. Probab. 16 (2006) 2, 827–852.
- [3] R.L. Karandikar, On pathwise stochastic integration, Stochastic Process. Appl. 57 (1995) 1, 11–18.
- [4] I. Karatzas, S.E. Shreve, Methods of Mathematical Finance, Springer, New York, 1998.
- [5] M. Hu, S. Peng, On the representation theorem of G-expectations and paths of G-Brownian motion, Acta Math. Appl. Sini. Engl. Ser. 25 (2009) 3, 539–546.
- [6] W. Panyu, Multiple G-Itô integral in the G-expectation space, Preprint: arXiv:1012.0368v1, 2 Dec 2010.
- [7] S. Peng, G-expectation, G-Brownian motion and related stochastic calculus of Itô type, Stoch. Anal. Appl., Abel Symp., Springer Berlin 2 (2007), 541–567.
- [8] S. Peng, Law of large numbers and central limit theorem under nonlinear expectations, Preprint: arXiv:0702358v1, 13 Feb 2007.
- [9] S. Peng, G-Brownian motion and dynamic risk measure under volatility uncertainty, Preprint: arXiv:0711.2834v1, 19 Nov 2007.
- [10] S. Peng, Nonlinear expectations and stochastic calculus under uncertainty with robust central limit theorem and G-Brownian motion, Preprint: arXiv:1002.4546v1, 24 Feb 2010.
- [11] H.M. Soner, N.Touzi, J.Zhang, Quasi-sure stochastic analysis through aggregation, Electron. J. Probab. 16 (2011) 67, 1844–1879.
- [12] N. Wiener, The homogeneous chaos, Amer. J. Math. 60 (1938), 897–936.
- [13] J. Xu, B. Zhang, Martingale characterization of G-Brownian motion, Stochastic Process. Appl. 119 (2009) 1, 232–248.
Typ dokumentu
Bibliografia
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