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

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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