Extremes of Nonstationary Harmonizable Processes

M. Grigoriu ()
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M. Grigoriu: Cornell University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 1, 1-29

Abstract: 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.

Keywords: Extremes of random processes; Finite dimensional distributions; Finite dimensional (FD) models; Generalized spectral density; Nonstationary processes; Weak convergence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10138-w

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