Some asymptotic properties of the hybrids of empirical and partial-sum processes. (English) Zbl 1143.60326

Alvarez-Andrade, Sergio

Rev. Mat. Iberoam. 24, No. 1, 31-41 (2008).

Summary: 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 \[ \bar{A}_n(t)=\sum _{1\leq i \leq n} H(X_i)1_{\{X_i\leq t\}} \epsilon_i, - \infty < t < \infty , \] namely by using knowing results on empirical process and Brownian local times.

MSC:

60J55	Local time and additive functionals
60F15	Strong limit theorems
60F17	Functional limit theorems; invariance principles
62G30	Order statistics; empirical distribution functions

Keywords:

local times; compensated Poisson process; hybrids of empirical and partial-sum processes; Brownian motion

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