Large and Moderate Deviations for Empirical Density Fields of Stochastic Seir Epidemics with Vertex-Dependent Transition Rates

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-03-09 DOI:10.1007/s11118-024-10133-9

Xiaofeng Xue, Xueting Yin

引用次数: 0

Abstract

In this paper, we are concerned with stochastic susceptible-exposed-infected-removed epidemics on complete graphs with vertex-dependent transition rates. Large and moderate deviations of empirical density fields of our models are given. Proofs of our main results utilize exponential martingale strategies. In the proof of the moderate deviation principle, we introduce an iteration approach to check the exponential tightness of scaled density fields of our processes. As an application of our main results, moderate deviations of a family of hitting times of our processes are also given.

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顶点依赖转换率的随机 Seir 流行病经验密度场的大偏差和中偏差

在本文中，我们关注的是完整图上的随机易感-暴露-感染-移除流行病，其转换率取决于顶点。本文给出了我们模型的经验密度场的大偏差和中等偏差。我们主要结果的证明采用了指数马丁格尔策略。在中等偏差原理的证明中，我们引入了一种迭代方法来检查我们过程的缩放密度场的指数紧密性。作为我们主要结果的一个应用，我们还给出了我们过程的一系列命中时间的适度偏差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.