Lithuanian Mathematical Journal

, Volume 58, Issue 4, pp 457–479 | Cite as

Joint functional convergence of partial sums and maxima for linear processes*

  • Danijel KrizmanićEmail author


For linear processes with independent identically distributed innovations that are regularly varying with tail index α ∈ (0, 2), we study the functional convergence of the joint partial-sum and partial-maxima processes. We derive a functional limit theorem under certain assumptions on the coefficients of the linear processes, which enable the functional convergence in the space of ℝ2-valued càdlàg functions on [0, 1] with the Skorokhod weak M2 topology.We also obtain a joint convergence in the M2 topology on the first coordinate and in theM1 topology on the second coordinate.


extremal process functional limit theorem linear process regular variation Skorokhod M2 topology stable Lévy process 


60F17 60G52 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RijekaRijekaCroatia

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