Etienne Pienaar will present the Department of Statistical Science seminar with a talk entiteld, "First Passage Time Problems for Diffusion Processes: Trapping a Bivariate Diffusion"

Abstract: Using a bivariate diffusion model, it is possible to model the trajectories of animal movement using a compact set of stochastic differential equations. If one were able to monitor such movement continuously at a sufficiently high temporal resolution, one may fit such models by way of evaluating the transitional distribution of a model diffusion. Where high-resolution movement trajectory data cannot be obtained, however, researchers often resort to using camera traps in order to monitor the movements of species. Under a diffusion model, replicating such an observational scheme leads to an interesting first passage time problem.  Unfortunately, even for simple first passage time problems, the requisite distributions remain analytically intractable. As such, we resort to numerical techniques for analysing such first passage time problems. In particular, we demonstrate how a numerical scheme for solving a PDE under appropriately chosen boundary conditions can be adapted to analyse the first passage time distribution of a bivariate diffusion process in the presence of a trapping array using a synthetic example.