Normal approximations for discrete-time occupancy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Hodgkinson, Liam¹  McVinish, Ross¹  Pollett, Philip K.¹ 

[1] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia

关键词: Central limit theorem;    Network models;    Quantitative law of large numbers;    Spreading processes;    Stein's method;    Stochastic patch occupancy models;   

DOI  :  10.1016/j.spa.2020.05.016

来源: Elsevier

【 摘 要 】

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks literature, including stochastic patch occupancy models in ecology, network models in epidemiology, and a variety of dynamic random graph models. Bounds on the rate of convergence for a central limit theorem are obtained using Stein's method and moment inequalities on the deviation from an analogous deterministic model. As a consequence, our work also implies a uniform law of large numbers for a subclass of these processes. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free