Strong law and central limit theorem for a process between maxima and sums

W.Th.F. Hollander, den, G. Hooghiemstra, M.S. Keane, J.A.C. Resing

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    1 Citation (Scopus)

    Abstract

    We prove an invariance principle for the random process (X n ) n1 given by where (Y n ) n1 are i.i.d. random variables and ( n ) n are nonrandom numbers tending upward to 1 (both in ). This process interpolates between maxima ( n 0) and sums ( n 1). Depending on the distribution ofY n and on the rate at which n 1 the scaling behaviour exhibits different regimes. Our techniques are flexible and are applicable to more general types of iterative schemes. Fulltext Preview
    Original languageEnglish
    Pages (from-to)37-55
    Number of pages19
    JournalProbability Theory and Related Fields
    Volume90
    Issue number1
    DOIs
    Publication statusPublished - 1991

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