Naslov
On joint weak convergence of partial sum and maxima processes

Autori
Krizmanić, Danijel

Izvornik
Stochastics: An International Journal of Probability and Stochastic Processes (1744-2508) 92 (2020), 6; 876-899

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Functional limit theorem ; regular variation ; weak M1 topology ; extremal process ; Lévy process

Sažetak
For a strictly stationary sequence of random variables we derive 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 limiting process consists of an alpha-stable Lévy process and an extremal process. We also describe the dependence between these two components of the limit. The convergence takes place in the space of R^2- valued cadlag functions on [0, 1], with the Skorohod weak M1 topology. We further show that this topology in general can not be replaced by the stronger (standard) M1 topology.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA