Normal approximations for discrete-time occupancy processes

Liam Hodgkinson, Ross McVinish and Philip K. Pollett

Stochastic Processes and their Applications, 2020, vol. 130, issue 10, 6414-6444

Abstract: 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.

Keywords: Central limit theorem; Network models; Quantitative law of large numbers; Spreading processes; Stein’s method; Stochastic patch occupancy models (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.05.016

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