Power Levy motion: Correlations and relaxation

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

Abstract: Recently established, Power Levy Motion (PLM) is a versatile Levy-driven model for pure-jump diffusion processes. On the one hand, PLM displays a host of anomalous-diffusion properties. On the other hand, PLM is highly tractable, and it has several neat representations. PLM is the ‘Levy counterpart’ of Power Brownian Motion (PBM): the only diffusion process that is Gaussian, Markovian, and selfsimilar. This paper explores PLM correlations: it devises three extensions of corresponding PBM correlations; and it devises Poissonian correlations that emanate from the PLM jump-structure. Further exploring the jump-structure, the paper also unveils the inherent ‘relaxation duration’ of PLM. The correlation and relaxation results established here are for a general spatio-temporal transformation of Levy Motion. In particular, the general results apply to PLM, as well as to the Lamperti transformation of PLM — the Levy-driven Ornstein-Uhlenbeck process.

Keywords: Levy-driven models; Correlation extensions; Poissonian correlations; Relaxation durations (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125004169

DOI: 10.1016/j.physa.2025.130764

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