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An alternative proof of a theorem of Aldous concerning convergence in distribution for martingales. (English) Zbl 0954.60037

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXIII. Berlin: Springer. Lect. Notes Math. 1709, 334-338 (1999).
A new proof of a theorem of Aldous is given. It is proved that under some uniform integrability condition the convergence of the distributions of a sequence \((M^n)\) of martingales to the distribution of a continuous martingale \(M\) in the Meyer-Zheng topology of the Skorokhod space \(\mathbb{D}([0, 1];\mathbb{R})\) implies the same convergence in the Skorokhod topology.
For the entire collection see [Zbl 0924.00016].

MSC:

60G44 Martingales with continuous parameter
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