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Renewal theory for asymmetric $$U$$-statistics. (English) Zbl 1406.60041
Summary: We extend a functional limit theorem for symmetric $$U$$-statistics [R. G. Miller jun. and P. K. Sen, Ann. Math. Stat. 43, 31–41 (1972; Zbl 0238.62057)] to asymmetric $$U$$-statistics, and use this to show some renewal theory results for asymmetric $$U$$-statistics.
Some applications are given.

##### MSC:
 60F05 Central limit and other weak theorems 60F17 Functional limit theorems; invariance principles 60K05 Renewal theory
##### Keywords:
$$U$$-statistics; renewal theory; functional limit theorems
Full Text:
##### References:
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