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A renewal theorem for an urn model. (English) Zbl 0544.60042

Summary: For an urn model (arising typically in the sequential estimation of the size of a finite population), along with an invariance principle for a partial sequence of nonnegative random variables, a renewal theorem relating to some stopping times is established. A representation of these random variables in terms of linear combinations of some martingale- differences provides the key to a simple solution.

MSC:

60F17 Functional limit theorems; invariance principles
60G42 Martingales with discrete parameter
62L99 Sequential statistical methods
60K05 Renewal theory
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