engleski

Joint functional convergence of partial sum and maxima processes

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.

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

nije evidentirano