Opuscula Math. 33, no. 4 (2013), 647-666
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.
- Received: 2012-05-02.
- Revised: 2013-04-04.
- Accepted: 2013-04-05.