发表机构
Universitat Autònoma de Barcelona（巴塞罗那自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非约束Feller过程局部时场的空间结构，证明其长时间极限下空间轮廓由非可归一化平稳密度控制，时间涨落由Mittag-Leffler随机振幅支配，并给出占据时间的Darling-Kac涨落及幂次观测量的平方Bessel型极限，为无穷遍历理论提供统一框架。
AI 中文摘要
我们研究非约束Feller过程的加性可观测量，该过程以非可归一化的平稳概率密度和具有无穷均值的返回时间为特征。在确定性重标度之后，该过程等价于平方Bessel过程，但我们在此聚焦于一个问题：其局部时场的空间结构。我们证明，在长时间极限下，局部时具有因子分解性质。其空间轮廓由非可归一化的平稳密度控制，而其时间涨落则由单个Mittag-Leffler随机振幅所支配。因此，局部时的归一化空间相关性收敛到一个与两个观测水平无关的普适常数。有限区间的占据时间作为推论随之得出，并展现出Darling-Kac涨落。相反，不可积的幂次可观测量则表现出自相似的平方Bessel型极限，而非Mittag-Leffler统计。这种空间场视角为状态依赖乘性噪声下的无穷遍历理论提供了一个统一框架。
英文摘要
We study additive observables of a non-confined Feller process characterized by a non- normalizable stationary probability density and return times with infinite mean. The process is equivalent, after a deterministic rescaling, to a squared Bessel process, but we focus here on a question: the spatial structure of its local-time field. We show that the local time admits a fac- torization in the long time limit. Its spatial profile is governed by the non-normalizable stationary density, whereas its temporal fluctuations are controlled by a single Mittag-Leffler random ampli- tude. As a consequence, normalized spatial correlations of the local time converge to a universal constant independent of the two observation levels. Occupation times of finite intervals follow as corollaries and display Darling-Kac fluctuations. In contrast, non-integrable power observables exhibit self-similar squared-Bessel-type limits rather than Mittag-Leffler statistics. This spatial- field perspective provides a unifying framework for infinite ergodic theory under state-dependent multiplicative noise.
