On functional weak convergence for partial sum processes

Danijel Krizmanic (University of Rijeka)

Abstract


For a strictly stationary sequence of regularly varying random variables we study functional weak convergence of partial sum processes in the space $D[0,1]$ with the $J_{1}$ topology. Under the strong mixing condition, we identify necessary and sufficient conditions for such convergence in terms of the corresponding extremal index. We also give conditions under which the regular variation property is a necessary condition for this functional convergence in the case of weak dependence.

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Pages: 1-12

Publication Date: August 26, 2014

DOI: 10.1214/ECP.v19-3686

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