Renewal theory for asymmetric $U$-statistics

TL;DR

This paper extends a functional limit theorem to asymmetric U-statistics and applies it to renewal theory, providing new insights and applications in the field.

Contribution

The paper introduces a functional limit theorem for asymmetric U-statistics, expanding the theoretical framework beyond symmetric cases.

Findings

Extended limit theorem to asymmetric U-statistics

Established renewal theory results for asymmetric U-statistics

Provided applications demonstrating the theory's utility

Abstract

We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics. Some applications are given.