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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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