Opuscula Math. 33, no. 4 (2013), 647-666
http://dx.doi.org/10.7494/OpMath.2013.33.4.647
Opuscula Mathematica
Chaotic expansion in the G-expectation space
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.
- 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.
