7 papers
Critical non-local spatial branching processes with infinite variance conditioned on survival
Natalia Cardona-Tobón, Andreas E. Kyprianou, Pedro MartÃn-Chávez
We consider the setting of either a general non-local branching particle process or a general non-local superprocess. Under the assumption that the mean semigroup has a Perron-Frob…
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…
A Unified Framework from Boltzmann Transport to Proton Treatment Planning
Andreas E. Kyprianou, Aaron Pim, Tristan Pryer
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on th…
The Brownian marble
Samuel G. G. Johnston, Andreas Kyprianou, Tim Rogers +1
Let be a measurable function. Consider coalescing Brownian motions started from every point in the subset of $[0,\inf…
Norm-dependent Lamperti-type MAP representations of stable processes and Brownian motions in the orthant
Andreas E. Kyprianou, Harry S. Mantelos, Victor Rivero
We start by remarking a one-to-one correspondence between self-similar Markov processes (ssMps) on a Banach space and Markov additive processes (MAPs) that is analogous to the well…
The strong law of large numbers and a functional central limit theorem for general Markov additive processes
Andreas E. Kyprianou, Victor Rivero
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and inde…