A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments.

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CWI
CWI. Probability, Networks and Algorithms [PNA]

van Zanten, H. (1998). A multivariate central limit theorem for continuous local martingales. CWI. Probability, Networks and Algorithms [PNA]. CWI.