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Limiting distribution of sums of nonnegative stationary random variables

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Summary

Let {X n,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatS n=Xn,1+…+X n,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {f n(x)∼ defined on a stationary sequence {X j∼, whereX n.f=fn(Xj). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type.

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Authors and Affiliations

  1. New York University, New York, USA

    Simeon M. Berman

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  1. Simeon M. Berman
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Additional information

This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Sciences Foundation, Grant MCS 82-01119.

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Berman, S.M. Limiting distribution of sums of nonnegative stationary random variables. Ann Inst Stat Math 36, 301–321 (1984). https://doi.org/10.1007/BF02481972

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  • DOI: https://doi.org/10.1007/BF02481972

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