Abstract
If $X^{(n)}$ is a sequence of semimartingales, converging to a semimartingale $X$, and such that $\lbrack X^{(n)}, X^{(n)}\rbrack$ converges to $\lbrack X, X\rbrack$, then all higher-order variations and all the iterated integrals of $X^{(n)}$ converge jointly to the respective functionals of $X$.
Citation
Florin Avram. "Weak Convergence of the Variations, Iterated Integrals and Doleans-Dade Exponentials of Sequences of Semimartingales." Ann. Probab. 16 (1) 246 - 250, January, 1988. https://doi.org/10.1214/aop/1176991898
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