发表机构
National and Kapodistrian University of Athens; CentraleSupélec, Université Paris-Saclay（雅典国立卡波迪斯特里阿斯大学; 巴黎萨克雷大学中央理工-高等电力学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在标准博雷尔状态空间上的离散马尔可夫更新理论，利用向量值逗留时间等。通过马尔可夫更新势提供多种表示，确定半马尔可夫场的马尔可夫增强及准则，建立分层逆更新理论并给出相关极限与估计，连接了多方面内容。
AI 中文摘要
我们在标准博雷尔状态空间上发展了一种离散马尔可夫更新理论，具有向量值逗留时间和在\(\N^d\)上的下矩形观测。马尔可夫更新势是一个核值卷积预解式，为半马尔可夫转移、首达律、占有测度和奖励提供统一表示。在部分有序格上观测的半马尔可夫场通常不是马尔可夫的，我们通过向后递归向量确定其规范马尔可夫增强，并给出增强可投影回原始状态空间的特殊情况下的可合并性准则。下矩形顺序导致分层逆更新理论，方向单纯形被分解为速率决定单元，在具有唯一活动坐标的单元上有高斯极限，在其界面上有相关高斯场的最小值。我们建立了函数逆极限、临界界面极限和逆偏差的对数估计。精确时间势从马尔可夫加性核的傅里叶 - 拉普拉斯扰动的算子理论局部定理获得，而再生定理给出相应的算术格类形式。结果将马尔可夫更新方程、多参数马尔可夫结构和由矩形观测诱导的局部渐近几何联系起来。
英文摘要
We develop stratified renewal theorems for multi-time observations of Markov-additive paths on standard Borel state spaces with nonnegative integer vector increments. Horizon directions with the same active constraints form strata. A compact-uniform inverse expansion yields a global limit in a topology combining hypi-convergence with exact restrictions to each stratum. At Brownian scale, the central theorem determines the joint terminal-edge law at fixed finite families of critical horizons about a common direction, under nondegenerate pairwise Gaussian contrasts. One Gaussian vector selects the exiting coordinates. Selections of the same coordinate at the same threshold share an edge; different selected pairs carry conditionally independent equilibrium marks. These marks retain both endpoint states, the full increment, age and overshoot. Under total-variation convergence of the state marginal to stationarity, pointwise scalar renewal convergence in total variation suffices for the marked argument. Regenerative conditions provide explicit criteria. Stationary scalar level processes retain dependence at fixed integer offsets. Under additional moment conditions, a second-order allocation theorem localizes optimal budgets and, with the marked hypotheses and nonsingular Gaussian contrasts, yields a cost-weighted equilibrium-edge mixture. An exact covariance criterion links uniform tightness of the unperturbed inverse field to the absence of a square-root allocation loss. Finite, denumerable and continuous modulating environments are included.
Commentsmanuscript 53 pages
