发表机构
Nankai University; Beijing Institute of Technology（南开大学; 北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究具有次指数跳跃的中心化Lévy过程的一致局部大偏差渐近性，在更弱矩假设下得到相关极限等式，为已有离散时间结果提供连续时间的一致类似结论。
AI 中文摘要
本文致力于统一具有次指数跳跃的中心化Lévy过程X的一致局部大偏差渐近性。结果表明，对任意θ,δ₀>0及K≥0，当t→∞时，sup_{x≥θt} sup_{|y|≤Kb(x)} sup_{δ∈[δ₀,∞]} sup_{0<s≤t} |P(Xₛ∈(x−y,x−y+δ])/(s·P(X₁∈(x,x+δ]))−1|=0，其中自然尺度函数b满足多项式增长条件。该成果为Denisov等人[Ann. Probab.,2008]的结果提供了连续时间且同时一致的类似结论，且在更弱的矩假设下成立。
英文摘要
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 $K\geq0$, $$\lim_{t\to\infty}\sup_{x\geqθt}\sup_{|y|\leq Kb(x)}\sup_{δ\in[δ_0,\infty]}\sup_{0<s\leq t}\bigg|\frac{\mathbf P\big(X_s\in(x-y,x-y+δ]\big)}{s\cdot\mathbf P\big(X_1\in(x,x+δ]\big)}-1\bigg|=0,$$ 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.
Comments25 pages: In the latest version, Condition 1.1(3) has been weakened, and more detailed explanations have been added to Condition 1.1. We have also included a new Corollary 1.4. All comments and suggestions are very welcome!
