On strong forms of weak convergence

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Abstract

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence, and are non-topological in nature. We give Storokhod representation results for two of these modes of convergence, and give applications to sufficient statistics and conditioned Markov processes, which are more difficult to obtain using weak convergence.

Keywords

Convergence in distribution
Skorokhod representation
Total variation metric

MSC

60B10

MSC

60J25
60J27 60H10
62B05

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