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Power Levy motion: Correlations and relaxation

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  • Eliazar, Iddo

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.

Suggested Citation

  • Eliazar, Iddo, 2025. "Power Levy motion: Correlations and relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125004169
    DOI: 10.1016/j.physa.2025.130764
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