"Asymptotic independence and additive functionals"

Endre Csáki and Antónia Földes

Summary: A strong approximation result is proved for the partial sum process of i.i.d. sequence of vectors having dependent components, where the components of the approximating process are independent. This result is applied for additive functionals of random walks in one and two dimensions.

Keywords: Asymptotic independence; random walk; additive functionals; invariance principle.

AMS 1991 subject classification: Primary 60J55; Secondary 60F15, 60F17, 60J15.