Speaker
Description
We study the long-time behaviour of a stochastic model for compartmentalised receptor signalling motivated by the trafficking of G protein-coupled receptors. The model describes the evolution of several chemical species distributed between the plasma membrane and a random population of endosomes. Chemical reactions follow deterministic dynamics inside each compartment, while stochastic events create endosomes by internalisation and recycle them back to the membrane. This leads to a piecewise deterministic Markov process with a variable number of compartments.
Using techniques inspired by the theory of Markov switching systems, we analyse the stability properties of the process. Under suitable contraction assumptions on the reaction dynamics, we prove the existence and uniqueness of a stationary distribution and establish exponential convergence in Wasserstein distance by a coupling argument. We also investigate exponential convergence in total variation using Harris theorem and identify structural conditions ensuring the existence of accessible Doeblin points.
