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Keywords = Gauss and Levy noises

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22 pages, 750 KiB  
Article
Levy Noise Affects Ornstein–Uhlenbeck Memory
by Iddo Eliazar
Entropy 2025, 27(2), 157; https://doi.org/10.3390/e27020157 - 2 Feb 2025
Cited by 2 | Viewed by 1041
Abstract
This paper investigates the memory of the Ornstein–Uhlenbeck process (OUP) via three ratios of the OUP increments: signal-to-noise, noise-to-noise, and tail-to-tail. Intuition suggests the following points: (1) changing the noise that drives the OUP from Gauss to Levy will not affect the memory, [...] Read more.
This paper investigates the memory of the Ornstein–Uhlenbeck process (OUP) via three ratios of the OUP increments: signal-to-noise, noise-to-noise, and tail-to-tail. Intuition suggests the following points: (1) changing the noise that drives the OUP from Gauss to Levy will not affect the memory, as both noises share the common ‘independent increments’ property; (2) changing the auto-correlation of the OUP from exponential to slowly decaying will affect the memory, as the change yields a process with long-range correlations; and (3) with regard to Levy driving noise, the greater the noise fluctuations, the noisier the prediction of the OUP increments. This paper shows that intuition is plain wrong. Indeed, a detailed analysis establishes that for each of the three above-mentioned points, the very converse holds. Hence, Levy noise has a significant and counter-intuitive effect on Ornstein–Uhlenbeck memory. Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
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