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On weak convergence of sequences of continuous local martingales. (English) Zbl 0609.60055
Author’s summary: Let \(\{M^ n(t)\}_{n=1,2,...}\) be a sequence of Hilbert space valued continuous local martingales. We give a necessary and sufficient condition for which \(\{M^ n\}\) is tight in C in terms of \(\{<M^ n>\}\). Using this result we show the preservation of the local martingale property under the weak convergence in C of \(\{M^ n\}\).
Reviewer: Chou Chingsung

MSC:
60G44 Martingales with continuous parameter
60F05 Central limit and other weak theorems
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