On Strong Forms of Weak Convergence
نویسنده
چکیده
We discuss three forms of convergence in distribution which are stronger than the normal weak convergence. They have the advantage that they are non-topological in nature and are inherited by discontinuous functions of the original random variables—clearly an improvement on ‘normal’ weak convergence. We give necessary and sufficient conditions for the three types of convergence and go on to give some applications which are very hard to prove in a more restricted setting. CONVERGENCE IN DISTRIBUTION; SKOROKHOD REPRESENTATION; TOTAL VARIATION METRIC. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60B10 SECONDARY 60J25, 60J27 60H10, 62B05
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