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Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems

Livieri, Giulia, Lillo, Fabrizio, Marmi, Stefano, Solomko, Anton and Vaienti, Sandro (2023) Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems. Journal of Statistical Physics, 190 (10). ISSN 0022-4715

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Identification Number: 10.1007/s10955-023-03160-0


We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average Lyapunov exponent depends continuously on the Markov chain parameters. Representing the Markov chain in terms of random transformation enables us to state and prove the Central Limit Theorem, the large deviation principle, and the Berry-Esséen inequality. We perform a multifractal analysis for the invariant and the stationary measures, and we prove Gumbel’s law for the Markov chain with an extreme index equal to 1.

Item Type: Article
Additional Information: © 2023 The Author(s)
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics
Date Deposited: 27 Sep 2023 15:27
Last Modified: 08 Jul 2024 00:54

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