Distributed-order (q,τ)-deformed Lévy processes and their spectral properties
Abstrak
Lévy processes play a central role in stochastic modeling, providing a unifying framework for jump dynamics, anomalous diffusion, and heavy-tailed phenomena across physics and applied sciences. We propose a novel framework for (q,τ,α,β)-generalized Lévy processes, extending fractional and tempered stable models with (q,τ)-Gamma and (q,τ)-Mittag--Leffler functions. The construction uses Laplace transforms of (q,τ)-inverse subordinators combined with the Lévy--Khintchine representation to obtain explicit expressions for characteristic functions. Numerical results show how variations in q and τ affect Γq,τ(x) and Eβ(q,τ)(z), leading to slower relaxation, heavier tails, and enhanced memory effects relative to classical counterparts. These outcomes demonstrate that (q,τ)-deformation provides a flexible mechanism for modeling anomalous diffusion, nonlocal dynamics, and heavy-tailed processes relevant in physics, finance, and geophysics.
Penulis (2)
I. Aldawish
Rabha W. Ibrahim
Akses Cepat
- Tahun Terbit
- 2025
- Bahasa
- en
- Total Sitasi
- 4×
- Sumber Database
- Semantic Scholar
- DOI
- 10.3389/fphy.2025.1647182
- Akses
- Open Access ✓