Convergence to Lévy stable processes under some weak dependence conditions

Details Convergence to Lévy stable processes under some weak dependence conditions Convergence to Lévy stable processes under some weak dependence conditions

2009-07-07

arxiv.org/abs/0907.1185v2

Stochastic Processes and their Applications 120 (2010) 1629--1650

Mathematics

Probability

Change of the title. Minor revisions

Scientific paper

10.1016/j.spa.2010.05.010

For a strictly stationary sequence of random vectors in $\mathbb{R}^d$ we
study convergence of partial sum processes to L\'evy 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.

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