[hal-00174789, v2] Non-central convergence of multiple integrals
نویسندگان
چکیده
Abstract: Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2, and let n > 2 be a fixed even integer. Consider a sequence {Fk}k>1 of square integrable random variables, belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that Fk converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k )− 12E(F 3 k ) → 12ν2 − 48ν.
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