The Central Limit Theorem is a statistical concept applied to large data distributions. It says that as you randomly sample data from a distribution, the means and standard deviations of the samples ...

Stochastic processes form the backbone of modern probability theory, describing systems that evolve randomly over time or space. They are instrumental in areas ranging from statistical physics to ...

In this paper, we consider functional limit theorems for Poisson cluster processes. We first present a maximal inequality for Poisson cluster processes. Then we establish a functional central limit ...

We consider a stochastic SIR (susceptible → infective → recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph ...