Stable limits for associated regularly varying sequences

TL;DR

This paper establishes conditions under which partial sums of associated, regularly varying stationary sequences converge to a stable distribution, extending to functional convergence in Skorokhod's $M_1$ topology.

Contribution

It provides new limit theorems for associated, regularly varying sequences, including functional convergence results.

Findings

Partial sums converge to a stable law under specified conditions.

Extension to functional convergence in Skorokhod's $M_1$ topology.

Applicable to a broad class of associated, regularly varying sequences.

Abstract

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a stable, non-Gaussian limit. The obtained limit theorem admits a natural extension to the functional convergence in Skorokhod's $M_1$ topology.