Naslov
A note on joint functional convergence of partial sum and maxima for linear processes

Autori
Krizmanić, Danijel

Izvornik
Statistics & probability letters (0167-7152) 138 (2018), 1; 42-46

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

Ključne riječi
Functional limit theorem ; Regular variation ; Stable Lévy process ; Extremal process ; M2 topology ; Linear process

Sažetak
Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index α∈(0, 2), a functional limit theorem with the Skorohod weak M2 topology has been obtained. In this paper we show that, if all the coefficients of the linear processes are of the same sign, the functional convergence holds in the stronger topology, i.e. in the Skorohod weak M1 topology on the space of R^2-valued càdlàg functions on [0, 1].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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