engleski

Functional limit theorem with the M_1 topology

We show that for a strictly stationary, regularly varying sequence of random variables for which clusters of high-threshold excesses can be broken down into asymptotically independent blocks, the properly centered partial sum process converges to a stable Levy process in the space D[0, 1] endowed with Skorohod's M_1 topology under the condition that all extremes within one such cluster have the same sign. The limiting process is characterized in terms of its characteristic triple.

regular variation; M_1 topology; weak dependence; functional limit theorem

nije evidentirano