engleski

Functional convergence of multivariate partial maxima processes

For a strictly stationary sequence of R^{; ; d}; ; _{; ; +}; ; valued random vectors (X_n) we derive functional convergence of the partial maxima stochastic process M_n(t) =max{; ; X_i/a_n : i=1, ..., \lfloor nt \rfloor}; ; , t \in [0, 1], under joint regular variation and weak dependence conditions, where (a_n) is a sequence of positive real numbers such that nP(||X1|| > an)->1 as n->1. The limit process is an extremal process, and the convergence takes place in the space of R^{; ; d}; ; _{; ; +}; ; valued cadlag functions on [0, 1], with the standard (or strong) Skorohod M_1 topology when d = 1 and weak Skorohod M_1 topology when d >= 2.

functional limit theorem ; regular variation ; M1 topology ; extremal process

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