Opuscula Math. 33, no. 4 (2013), 647-666

Opuscula Mathematica

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.

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  • 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
  • Received: 2012-05-02.
  • Revised: 2013-04-04.
  • Accepted: 2013-04-05.
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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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