A Multivariate Functional Limit Theorem in Weak M1 Topology

2013/08/16 by Bojan Basrak, Basrak, Bojan, Danijel Krizmanić +1
Mathematics · #60F17 #60G52 #60G55 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60G52 #msc:60G55

paper · pdf · doi:10.48550/arxiv.1308.3624

22 pages, 1 figure. arXiv admin note: text overlap with arXiv:1001.1345

arxiv created 2013/08/16 · arxiv updated 2013/08/19

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.

Citations

• A functional limit theorem for dependent sequences with infinite variance stable limits

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