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Normal approximations for discrete-time occupancy processes

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  • Hodgkinson, Liam
  • McVinish, Ross
  • Pollett, Philip K.

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.

Suggested Citation

  • Hodgkinson, Liam & McVinish, Ross & Pollett, Philip K., 2020. "Normal approximations for discrete-time occupancy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6414-6444.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6414-6444
    DOI: 10.1016/j.spa.2020.05.016
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    References listed on IDEAS

    as
    1. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
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