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Extremes of Nonstationary Harmonizable Processes

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  • M. Grigoriu

    (Cornell University)

Abstract

Finite dimensional (FD) models $$X_d$$ X d , i.e., deterministic functions of time and finite sets of d random variables, are developed for a class of nonstationary processes X, referred to as harmonizable. The FD models are based on Karhunen-Loève and spectral representations of X. Conditions are established under which distributions of extremes of X can be approximated by those of extremes of $$X_d$$ X d provided that the stochastic dimension d is sufficiently large. FD models are constructed for monochromatic, Brownian motion and Ornstein-Uhlenbeck processes. Numerical results suggest that their extremes can be used as surrogates for the extremes of these processes in agreement with our theoretical findings.

Suggested Citation

  • M. Grigoriu, 2025. "Extremes of Nonstationary Harmonizable Processes," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-29, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-025-10138-w
    DOI: 10.1007/s11009-025-10138-w
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    References listed on IDEAS

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    1. Samorodnitsky, Gennady, 1991. "Probability tails of Gaussian extrema," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 55-84, June.
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