Revista Matemática Iberoamericana


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Volume 24, Issue 1, 2008, pp. 31–41
DOI: 10.4171/RMI/528

Published online: 2008-04-30

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

Sergio Alvarez-Andrade[1]

(1) Université de Technologie de Compiègne, France

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.

Keywords: Local times, compensated Poisson process, hybrids of empirical and partialsum processes, Brownian motion

Alvarez-Andrade Sergio: Some asymptotic properties of the hybrids of empirical and partial-sum processes. Rev. Mat. Iberoamericana 24 (2008), 31-41. doi: 10.4171/RMI/528