Asymptotic behaviour of branching piecewise deterministic Markov processes

Branching piecewise deterministic Markov processes (PDMPs) can be used to model a range of real-world processes such as neutron transport, cell division and protein polymerisation. Thus, it is crucial to understand their long-term behaviour. In this talk, I will introduce a general class of branching PDMPs in a bounded domain and show that under mild assumptions, a Perron Frobenius type result holds for the average of the process. That is, I will prove the existence of the leading eigenvalue and corresponding eigenfunctions of the linear semigroup, and show that they characterise the asymptotic macroscopic behaviour of the system. I will also discuss a new simulation technique based on population control methods that can be used to estimate these quantities.