# Some asymptotic properties of the hybrids of empirical and partial-sum processes

### Sergio Alvarez-Andrade

Université de Technologie de Compiègne, France

## Abstract

The motivation of this paper is to study some properties of the local times (when it exists) of the hybrids of empirical and partial-sum processes defined by

\bar{A}_n(t)=\sum_{1\leq i \leq n} H(X_i)1_{\{X_i\leq t\}} \epsilon_i, \quad - \infty #x003C; t #x003C; \infty ,

namely by using knowing results on empirical process and Brownian local times.

## Cite this article

Sergio Alvarez-Andrade, Some asymptotic properties of the hybrids of empirical and partial-sum processes. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 31–41

DOI 10.4171/RMI/528