发表机构
Technische Universität Braunschweig; Weierstrass Institute Berlin（不伦瑞克工业大学; 柏林魏尔斯特拉斯研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对接触过程型感染动力学，提出超越随机占优的局部到全局比较准则，证明感染规则可排序，并发现连续时间接触过程占优相关模型而离散版本不占优。
AI 中文摘要
我们研究了在 $\mathbb Z^d$ 上具有一般局部传播机制的接触过程型感染动力学的比较不等式。所考虑的過程包括离散时间定向渗流模型和连续时间接触过程，其中感染事件可能传播到随机的、可能相关的邻居集合。我们的主要结果应用了超越随机占优的局部到全局比较准则：如果一个局部感染规则比另一个更可能击中邻居的每个非空测试集，则相应的过程在所有时刻具有更大的生存概率。我们比较了经典独立感染模型与可交换固定预算、全有或全无以及突发型感染机制，推导出例如有限时间和无限时间生存概率以及停止时间分布的排序。在连续时间中，我们进一步获得了可交换感染律的临界生存阈值的结果。结果表明，具有相同或可比较的平均场感染强度的感染过程，在考虑空间几何后，仍然可以在随机层面上被严格排序。此外，经典连续时间接触过程支配多种相关的连续时间模型，而其最自然的离散时间版本——伯努利定向渗流——相对于相关的离散时间模型并不占优。
英文摘要
We study comparison inequalities for contact-process-type infection dynamics on $\mathbb Z^d$ with general local transmission mechanisms. The processes considered include both discrete-time oriented-percolation models and continuous-time contact processes in which infection events may transmit to random, possibly correlated sets of neighbouring sites. Our main results apply local-to-global comparison criteria beyond stochastic domination: if one local infection rule is more likely than another to hit every non-empty test set of neighbours, then the corresponding process has larger survival probabilities at all times. We compare classical independent-infection models with exchangeable fixed-budget, all-or-nothing, and burst-type infection mechanisms, deriving orderings for example of finite-time and infinite-time survival probabilities and stopping-time distributions. In continuous time, we further obtain consequences for critical survival thresholds of exchangeable infection laws. The results show that infection processes with identical or comparable mean-field infection intensity can nevertheless be rigorously ordered at the stochastic level once spatial geometry is taken into account. Additionally, it turns out that the classical continuous-time contact process dominates a variety of related continuous-time models, whereas its most natural discrete-time version, Bernoulli oriented percolation, is not dominant with respect to related discrete-time models.
Comments13 pages, 2 figures
