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In this paper, motivated by mathematic finance we introduce the multipleG-It\^{o} integral in the G-expectation space, then investigate how tocalculate. We get the the relationship between Hermite polynomials and multipleG-It\^{o} integrals which is a natural extension of the classical resultobtained by It\^{o} in 1951.

Multiple G-It\^{o} integral in the G-expectation space