Proton beam therapy is a relatively modern way of treating cancer. In short, protons are accelerated to around 2/3 the speed of light and projected into the body in the direction of cancerous tissues. Subatomic interactions slow the protons down causing energy deposition into tissue. The less energy protons have, the greater the number of subatomic interactions and the greater the rate at which energy is deposed. This results in the proton beam having an approximate “end point” where the majority of the initial energy in the beam is deposited. Rather obviously, this needs to be positioned into cancerous tissues and accuracy is essential; in particular if the tumour is positioned next to or within organs/bones where irreparable damage could be caused by the proton beam. Modelling the deposition of energy into the human body is often undertaken using software not dissimilar to (if not actually the same as) the software used that simulates particle experiments in large accelerators such as CERN. Simulations essentially reconstruct every nuclear interaction, incorporating e.g. CT scan data, and can take hours to prepare and execute. Whilst reasonably accurate, such simulations do not allow for “on the fly adjustments” to be made as patients move through their course of treatment. The only known mathematical model for the way in which energy is deposited into the patient suffers from being one dimensional and does not connect directly to the underlying particle physics. In this talk we discuss what we believe to be the first mathematical model of a proton beam, grounded in the subatomic physics, taking the form of a (7+1)-dimensional SDE which has both diffusive and jump components. A fundamental modelling question of this class of SDEs pertains to constructing a well-defined meaning of “rate of energy deposition” in the three dimensions of space and how relates to Monte Carlo simulation. Ultimately this boils down to the existence of an occupation density for the SDE, which, in turn requires us to work with fundamental ideas from Malliavin calculus. This work is part of a larger body of research that is currently being undertaken in collaboration with the proton beam treatment centre at University College London Hospital.