Naslov
Joint functional convergence of partial sum and maxima processes

Autori
Krizmanić, Danijel

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
8th European Congress of Mathematics, 20–26 June 2021, Portorož, Slovenia, Book of Abstracts / - , 2021, 671-671

Skup
8th European Congres of Mathematics

Mjesto i datum
Portorož, Slovenija, 20.06.2021. - 26.06.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Functional convergence ; Partial sum ; Partial maxima, Joint regular variation ; Skorohod topology

Sažetak
For a strictly stationary sequence of random variables we study functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0, 2)$ and weak dependence conditions. The convergence takes place in the space of $\mathbb{;R};^{;2};$--valued cadlag functions on $[0, 1]$, with the Skorohod weak $M_{;1};$ topology, and the limiting process consists of an $\alpha$--stable Levy process and an extremal process. We also show that the weak $M_{;1};$ topology in general can not be replaced by the standard $M_{;1};$ topology.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA