engleski

Joint functional convergence of partial sums and maxima for linear processes

For linear processes with independent identically distributed innovations that are regularly varying with tail index alpha in (0, 2), we study functional convergence of the joint partial sum and partial maxima processes. We derive a functional limit theorem under certain assumptions on the coefficients of the linear processes which enable the functional convergence to hold in the space of R^2-valued cadlag functions on [0, 1] with the Skorohod weak M2 topology. Also a joint convergence in the M2 topology on the first coordinate and in the M1 topology on the second coordinate is obtained.

extremal process ; functional limit theorem ; linear process ; regular variation ; Skorohod M2 topology ; stable Levy process

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