A Multivariate Functional Limit Theorem in Weak M1 Topology

Bojan Basrak; Danijel Krizmanić

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arXiv · 1308.3624

A Multivariate Functional Limit Theorem in Weak M1 Topology

Bojan Basrak·Danijel Krizmanić

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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 R^d valued càdlàg functions endowed with the so-called weak M1 topology. The theory is illustrated on two examples. In particular, we demonstrate why such an extension of Skorohod's M1 topology is actually necessary for the limit theorem to hold.

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Bojan Basrak, Danijel Krizmanić. 2013-08-16. A Multivariate Functional Limit Theorem in Weak M1 Topology. https://arxiv.org/abs/1308.3624

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