Naslov
Functional weak convergence of partial maxima processes

Autori
Krizmanić, Danijel

Izvornik
Extremes (1386-1999) 19 (2016), 1; 7-23

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

Ključne riječi
extremal index ; functional limit theorem ; regular variation ; Skorohod J1 topology ; strong mixing ; weak convergence

Sažetak
For a strictly stationary sequence of nonnegative regularly varying random variables $(X_{; ; ; ; ; ; n}; ; ; ; ; ; )$ we study functional weak convergence of partial maxima processes $M_{; ; ; ; ; ; n}; ; ; ; ; ; (t) = \bigvee_{; ; ; ; ; ; i=1}; ; ; ; ; ; ^{; ; ; ; ; ; \lfloor nt \rfloor}; ; ; ; ; ; X_{; ; ; ; ; ; i}; ; ; ; ; ; , \, t \in [0, 1]$ in the space $D[0, 1]$ with the Skorohod $J_{; ; ; ; ; ; 1}; ; ; ; ; ; $ topology. Under the strong mixing condition, we give sufficient conditions for such convergence when clustering of large values do not occur. We apply this result to stochastic volatility processes. Further we give conditions under which the regular variation property is a necessary condition for $J_{; ; ; ; ; ; 1}; ; ; ; ; ; $ and $M_{; ; ; ; ; ; 1}; ; ; ; ; ; $ functional convergences in the case of weak dependence. We also prove that strong mixing implies the so- called Condition $\mathcal{; ; ; ; ; ; A}; ; ; ; ; ; (a_{; ; ; ; ; ; n}; ; ; ; ; ; )$ with the time component.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA