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Some limit theorems for rescaled Wick powers

By Alberto Lanconelli

Abstract

We establish the strong L 2 (P)-convergence of properly rescaled Wick powers as the power index tends to infinity. The explicit representation of such limit will also provide the convergence in distribution to normal and log-normal random variables. The proofs rely on some estimates for the L 2 (P)-norm of Wick products and on the properties of second quantization operators. Key words and phrases: Wick product, second quantization operator, convergence in distribution

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