5 papers
A moment approach to the law of large numbers for supercritical branching Markov processes
Christopher B. C. Dean, János Engländer, Emma Horton
We offer a new proof of the classical law of large numbers for a general class of branching Markov processes based on the asymptotic behaviour of the moments developed in \cite{bmo…
SDE-based Monte Carlo dose calculation for proton therapy validated against Geant4
Christopher B. C. Dean, Maria L. Pérez-Lara, Emma Horton +3
Objective: To assess the accuracy and computational performance of a stochastic differential equation (SDE)--based model for proton beam dose calculation by benchmarking against Ge…
Functional central limit theorems for non-local branching Markov processes
Christopher B. C. Dean, Emma Horton
The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We establish functional centr…
More on the asymptotic behaviour of moments of branching Markov processes
Christopher B. C. Dean, Emma Horton
Consider a branching Markov process, , with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attentio…
Functional limit theorems for Pólya urns with growing initial compositions
Christopher B. C. Dean
In this paper, we prove functional limit theorems for Pólya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent w…