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LetXi,n'i=1, ...n be a triangular array in the domain of attraction of a Lévy processX(t). Then the symmetric polynomial of orderk in theXi,n'$$\sum\limits_{1 \leqq i_1< i_2<  \ldots< i_k  \leqq [nt]} {X_{i_1 ,n}  X_{i_2 ,n}  \ldots  X_{i_k ,n} ,}$$ converges weakly to thekth order multiple integral with respect toX(t). Also, sums of powers of theXi,n converge jointly to the variations of the processX(t).

Symmetric polynomials of random variables attracted to an infinitely divisible law