Normal approximations for discrete-time occupancy processes

TL;DR

This paper develops normal approximation bounds for discrete-time occupancy processes, including models in ecology, epidemiology, and network theory, using Stein's method to establish convergence rates and a uniform law of large numbers.

Contribution

It introduces new bounds on the rate of convergence for CLTs in occupancy processes with product Bernoulli transition kernels, applicable to various complex network models.

Findings

Established convergence rates for CLTs in occupancy processes.

Derived a uniform law of large numbers for a subclass of models.

Applied Stein's method and moment inequalities for analysis.

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.