A Multivariate Functional Limit Theorem in Weak $$M_{1}$$ M 1 Topology

Bojan Basrak () and Danijel Krizmanić ()
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Bojan Basrak: University of Zagreb
Danijel Krizmanić: University of Rijeka

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 119-136

Abstract: Abstract We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of $$\mathbb R ^{d}$$ R d valued càdlàg functions endowed with the so-called weak $$M_{1}$$ M 1 topology. The theory is illustrated on two examples. In particular, we demonstrate why such an extension of Skorohod’s $$M_1$$ M 1 topology is actually necessary for the limit theorem to hold.

Keywords: Functional limit theorem; Regular variation; Stable Lévy process; Weak $$M_{1}$$ M 1 topology; 60F17; 60G52; 60G55 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0510-3

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