Convergence to Lévy stable processes under some weak dependence conditions

Abstract

For a strictly stationary sequence of random vectors in ${\mathbb{R}}^d$ we study convergence of partial sum processes to Lévy stable process in the Skorohod space with $J_1$-topology. We identify necessary and sufficient conditions for such convergence and provide sufficient conditions when the stationary sequence is strongly mixing.

Change of the title. Minor revisions

References in corpus (1)

• Recent advances in invariance principles for stationary sequences

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