English

A Multivariate Functional Limit Theorem in Weak M1 Topology

Probability 2013-08-19 v1

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 c\`{a}dl\`{a}g 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.

Keywords

Cite

@article{arxiv.1308.3624,
  title  = {A Multivariate Functional Limit Theorem in Weak M1 Topology},
  author = {Bojan Basrak and Danijel Krizmanić},
  journal= {arXiv preprint arXiv:1308.3624},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-22T01:10:26.000Z