Noncentral Convergence of Multiple
نویسندگان
چکیده
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 {F k } 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 F k converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k) − 12E(F 3 k) → 12ν 2 − 48ν.
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