📝 SummarXiv

Abstract

We develop numerical schemes and sensitivity methods for stochastic models of proton transport that couple energy loss, range straggling and angular diffusion. For the energy equation we introduce a logarithmic Milstein scheme that guarantees positivity and achieves strong order one convergence. For the angular dynamics we construct a Lie-group integrator. The combined method maintains the natural geometric invariants of the system. We formulate dose deposition as a regularised path-dependent functional, obtaining a pathwise sensitivity estimator that is consistent and implementable. Numerical experiments confirm that the proposed schemes achieve the expected convergence rates and provide stable estimates of dose sensitivities.