PreprintCC BY 4.0arXiv
Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps
Abstract
This paper is devoted to unifying the uniform local large-deviation asymptotics for a centered Lévy process X with subexponential jumps. Our results assert that for any θ,δ0>0 and K≥0, limt→∞supx≥θtsup|y|≤ Kb(x)supδ∈[δ0,∞]sup0<s≤ t|(P(Xs∈(x−y,x−y+δ]))/(s·P(X1∈(x,x+δ]))−1|=0, where the natural-scale function b satisfies a polynomial growth condition. This provides a continuous-time and simultaneously uniform analogue of the results of Denisov et al. [Ann. Probab., 2008], while being established under a weaker moment assumption.
Related
- Large Excursions of Reflected Lévy Processes: Local Asymptotics
- Local uniform asymptotics for a non-standard risk model and interplay of insurance and financial risks stemming by systemic factors
- A Class of Stochastic Partial Differential Equations with Jumps in Fluid Dynamics: Large and Moderate Deviation Asymptotics
- Coupling for one-dimensional subcritical and critical CBI processes with jumps
- First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps
BibTeX
@misc{wu2026uniform,
title = {{Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps}},
author = {Hao Wu and Wei Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.11637},
eprint = {2608.11637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps
AU - Hao Wu
AU - Wei Xu
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2608.11637
UR - https://arxiv.org/abs/2608.11637
AB - This paper is devoted to unifying the uniform local large-deviation asymptotics for a centered Lévy process X with subexponential jumps. Our results assert that for any θ,δ_0>0 and K≥0, lim_t→∞sup_x≥θtsup_|y|≤ Kb(x)sup_δ∈[δ_0,∞]sup_0<s≤ t|(P(X_s∈(x−y,x−y+δ]))/(s·P(X_1∈(x,x+δ]))−1|=0, where the natural-scale function b satisfies a polynomial growth condition. This provides a continuous-time and simultaneously uniform analogue of the results of Denisov et al. [Ann. Probab., 2008], while being established under a weaker moment assumption.
ER -