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Scaling limit of heavy tailed nearly unstable cumulative INAR($\infty$) processes and rough fractional diffusions
- Publication Year :
- 2024
-
Abstract
- In this paper, we investigated the scaling limit of heavy-tailed unstable cumulative INAR($\infty$) processes. These processes exhibit a power law tail of the form $n^{-(1+\alpha)}$, with $\alpha \in (\frac{1}{2}, 1)$, where the $\ell^1$ norm of the kernel vector is close to $1$. The result is in contrast to scaling limit of the continuous-time heavy tailed unstable Hawkes processes and the one of INAR($p$) processes. We show that the discrete-time scaling limit also has long-memory property and can also be seen as an integrated fractional Cox-Ingersoll-Ross process.<br />Comment: arXiv admin note: text overlap with arXiv:1504.03100 by other authors
- Subjects :
- Mathematics - Probability
60G22, 60F05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.11773
- Document Type :
- Working Paper