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 \(\mathbb R ^{d}\) valued càdlàg functions endowed with the so-called weak \(M_{1}\) topology. The theory is illustrated on two examples. In particular, we demonstrate why such an extension of Skorohod’s \(M_1\) topology is actually necessary for the limit theorem to hold.
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Acknowledgments
Bojan Basrak’s research was partially supported by the research grant MZOS nr. 037-0372790-2800 of the Croatian government.
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Basrak, B., Krizmanić, D. A Multivariate Functional Limit Theorem in Weak \(M_{1}\) Topology. J Theor Probab 28, 119–136 (2015). https://doi.org/10.1007/s10959-013-0510-3
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DOI: https://doi.org/10.1007/s10959-013-0510-3