Tail Behavior and Almost Sure Growth Rate of Superpositions of Ornstein–Uhlenbeck-type Processes

Danijel Grahovac () and Péter Kevei ()
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Danijel Grahovac: J. J. Strossmayer University of Osijek
Péter Kevei: University of Szeged

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-15

Abstract: Abstract In this paper, we consider sample path growth of superpositions of Ornstein–Uhlenbeck-type processes (supOU). SupOU processes are stationary infinitely divisible processes defined as integrals with respect to a random measure. They allow marginal distributions and correlations to be modeled independently. Our results show that the almost sure behavior is primarily governed by the tail of the marginal distribution. In particular, we obtain a general integral test for the sample path growth that covers both heavy-tailed and light-tailed scenarios. We also investigate the tail behavior of the marginal distributions in connection with the characteristics of the underlying random measure.

Keywords: SupOU processes; Infinitely divisible random measure; Integral test; Almost sure properties; Rate of growth; 60G17; 60F15; 60G55; 60G57 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01374-w

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