Opuscula Math. 33, no. 4 (2013), 647-666
Chaotic expansion in the G-expectation space
Hacène Boutabia
Imen Grabsia
Abstract.
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.
Keywords:
\(G\)-expectation, \(G\)-Brownian motion, \(G\)-multiple integrals, Hermite polynomials, \(G\)-Wiener chaos.
Mathematics Subject Classification:
60H10, 60H05, 60H30.
About the authors ▼
Hacène Boutabia
Laboratoire LaPS, Département de Mathématiques, Faculté des Sciences, Université Badji Mokhtar, Annaba 23000, Algéria
Imen Grabsia
Département de Mathématiques, Faculté des Sciences, Université Badji Mokhtar-Annaba 23000, Algéria
About the article ▼
Received: 2012-05-02.
Revised: 2013-04-04.
Accepted: 2013-04-05.
Cite this article as ▼
Hacène Boutabia, Imen Grabsia, Chaotic expansion in the G-expectation space, Opuscula Math. 33, no. 4 (2013), 647-666,
http://dx.doi.org/10.7494/OpMath.2013.33.4.647.
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